Table Of ContentUnusual photon isospin mixing and instantaneous Coulomb effects on the
thermodynamics of compact matter
∗
Ji-sheng Chen
Institute of Particle Physics & Physics Department,
Hua-Zhong Normal University, Wuhan 430079, People’s Republic of China
Ahiddenlocalsymmetryformalism withatwo-photoncountertermapproachisperformedbased
on the relativistic continuum quantum many-body theory. The underlying electromagnetic under-
screeningaswellasscreeningeffectsbetweentheelectricchargedpoint-likeelectronsandcomposite
protonsare discussed byanalyzing thein-mediumisospin mixingof Lorentzvectorwith scalar due
to electromagnetic photon. Besides the usual screening results, the main conclusion is that an
effective oscillatory instantaneous Coulomb potential between the like-charged collective electrons
contributes a very large negative term to the equation of state. This counterintuitive like-charged
attractionresultsfromthemodulationfactoroftheoppositechargedbaryonsuperfluidbackground.
7
The anomalous long distance quantum dragging effects between the collective electrons can be
0
induced in a compact Coulomb confinement environment. The physics is of the strongly coupling
0
characteristic in a specific diluteregime.
2
n PACSnumbers: 21.65.+f,11.30.Cp,21.10.Sf
a Keywords: universalthermodynamics,longrangeforce,statistical methods
J
3
2 I. INTRODUCTION fectthesingleparticleenergyspectrumasrecentlyfound
withthestudyofsomemirrornuclei,whichprovidesevi-
4 dencefortheinclusionofthe novelelectromagneticspin-
v Intriguingly, it is usually assumed that there is a uni-
orbit effect[6]. To our knowledge, the EM correlation is
8 form positive background to ensure the stability in dis-
stillachallengingtaskinmany-bodytheoryandevenfor
3 cussing the thermodynamics of electrons system. This is
0 the well-known (generalized) Thomson Problem for over finite nuclei[7].
9 acentury. Ofcourse,there isnotafinishedstandardan- Theeffectiverelativisticcontinuumnucleartheorypro-
0 swer up to now[1]. In nuclear physics, the status quo is vides a powerful theoretical framework to account for
5
aninverse one. Theelectronsareusuallytakenasauni- the various exotic many-body properties of neutron-star
0
/ formnegativechargedbackgroundandfurthertreatedas nuclear matter or finite nuclei[8, 9]. The pairing cor-
h theidealdegenerategaswiththenotionthatthe nuclear relation calculations of neutrons and protons in nuclear
-t forceisofelectricchargeindependent. Furthermore,itis matter inspired by the quite different empirical nega-
cl customarily accepted that the weak Coulomb contribu- tive scattering lengths in free space between nucleons
u tion is well known or screened out and can be turned off promote us to assume the spontaneous breaking anal-
n bytakingthepoint-likepictureofprotons. Whatphysics ogously to the EM U(1) gauge symmetry breaking con-
v: will be found or answered if considering the interactions ceptofAnderson-Higgsmechanisminordertogaugethe
i between the two opposite charged subsystems? infrared singularity[10, 11]. This is the Lorentz sponta-
X neous violation according to the standard notion, which
The realistic nuclear matter is subject to the long
r is currently the central topic of cosmology etc.[12, 13].
a range electromagnetic(EM) interaction. The infrared
The theoretical spinodal instability and uncertainty can
EM Coulomb force between the charged particles such
beremovedconsequentlywiththein-mediumLorentzvi-
as electrons and composite protons makes the discussion
olation notion.
ofthermodynamicsorequationofstates(EOS)evenmore
involved and may lead to rich physics[2, 3, 4, 5]. In ad- The electron density becomes very diluter(hence
dition to the (residual) strong interaction contribution stronglycorrelatingaccordingtostatisticalphysics)com-
to EOS, the EM fluctuation/correlation effects are very pared with the baryon density when one takes into ac-
important to the mechanical, thermal, chemical equilib- count the charge neutralized condition[11]. It remains
rium conditions and further influence the various trans- an intriguing task to deal with the strongly correlated
portpropertiesofthecompactstarnuclearmatterdueto electrons ground state energy simultaneously with that
Coulomb “frustration” effects (for example, see Refs. [5] ofnucleons,whichiscloselyrelatedwiththeneutronstar
and references therein). This kind of frustration effects crustorsupernovaexplosionphysicsinthediluteregime.
willleadtothestronglycoupledpicturephysicswhichbe- Needless to say, this is a fundamental/difficult problem
longstothenon-perturbativecontext. Thehithertoover- to tackle analytically in the general many-body context.
lookedbutimportantEMforcecanevensignificantlyaf- To address the charge neutralized strongly interact-
ingsystemthermodynamicswiththenetelectriccharged
chemical potential based on the relativistic continuum
field theory formalism, we propose a compensatory two-
∗[email protected] photon method with the Hidden Local Symmetry(HLS)
2
formalism to remove the infrared singularity. Surpris- In Eq.(2), the polarization tensor components are calcu-
ingly,theexactgroundstateenergysolutionofcollective lated via the following selfenergies
electronsmanifestsacounterintuivelongrangeattraction
picture in the strongly coupling limit, which is far from Πσ (k) =2g2T Tr 1 1 ,
the starting point in order to unveil/answer the realistic N,P σ /p−M∗(/p−k/)−M∗
physics motivation presented in Ref.[11]. Xp0 Zp (cid:20) (cid:21)
The plan of this work is as follows. In Section II, the Πσ−γ,µ(k) =eg T Tr 1 γµ 1 (3,)
irsaonsgpeinnmucilxeianrgfeoffrceec)t loefapdhinogtotnowuintdhesri-gscmraeemniensgonis(sahnoart- P σ Xp0 Zp (cid:20)/p−M∗ (/p−k/)−M∗(cid:21)
1 1
lyzed. The consequentnovelquantum fluctuation effects Πγ,µν(k) =e2T Tr γµ γν ,
P /p−M∗ (/p−k/)−M∗
on the strongly correlated electrons thermodynamics in Xp0 Zp (cid:20) (cid:21)
a dilute compact confinement environment is discussed
in Section III. The discussions are made in Section IV. with the shorthand notation p = d3p/(2π)3 and p0 =
The final SectionV presents the conclusion remarks. (2n+1)πTi+µ∗ while µ∗ and M∗ being the effective
R R
chemical potential and fermion mass, respectively. The
Πγ,µν fortheelectron-loopself-energyissimilartoΠγ,µν.
e P
II. ISOSPIN MIXING OF PHOTON WITH Thestandardcalculationsoftheself-energiesincluding
SIGMA MESON the Dirac and Fermi’s sea contribution at finite temper-
ature can be found in Ref.[16]. Here in this work, con-
To make the constructive two-photon Thomson Prob- centratingonthe density fluctuationeffects andrelevant
lem counterterm scheme presented in the next section physics, we present explicitly the Fermi sea’s contribu-
more comprehensive, we will firstly reveal the unusual tion of scalar meson self-energy and the σ − γ mixing
polarization properties that are often overlooked. The polarization tensor-0 component at T =0
discussions will give us a strong inspiration, i.e., there
∗
is the possible EM under(anti)-screening effects in addi- Πσ−γ,0(0,0) =−egσM k ,
tion to the usual screening in a compact environment. P π2 f
The expected conventional weak coupling perturbative g2 M∗
expansion and/or resummation based on the exclusive ΠσN,P(0,0) = 2πσ2 kfEf∗ +3M∗2lnk +E∗ , (4)
screening of normal state cannot be valid any more in f f#
(cid:2)
addressing the strongly coupling limit thermodynamics.
In addressing the low energy long wavelength ther- whereE∗ = k2+M∗2. FromEq.(4),onecanfindthat
f f
modynamics, it is a good approximation to take the the static limqit of the sigma meson self-energy is nega-
nucleon as a point-like particle according to the effec- tive ∼ −106MeV2 in a wide density and temperature
tive field theory’s idea[8]. With this picture, one can regime enhanced by the isospin degenerate factor “2” in
perform the polarization tensor calculation with the in- Eq.(3) due to the doping effects of neutrons. This can
medium protons[14]. Essentially, according to particle be attributed to the different isospin vector and scalar
physics, one can introduce the isospin concept for pho- fluctuation behaviors of QCD[16].
ton γ. Therefore we can study the nontrivial in-medium The standard Thomas-Fermi/Debye screening masses
isospinmixingofγ andsigmamesonσ followingthewell are closely associated with EOS, which are defined ac-
discussedσ−ω mixingetc.,fromwhichthefullpropaga- cording to the static infrared limit of the relevant self-
tors of γ and σ can be simultaneously determined with energies[17]. Thestatic limit ofthe e(P)-loopself-energy
the mixing polarization tensor Π, a 5×5 matrix[15]. is the familiar formalism
With Π, the dielectric function inthe presence ofmix-
ingtodeterminethecollectivemodesorstudythescreen- Π00(0,0)=−e2k E∗. (5)
ing effects is π2 f f
ǫ(k ,|k|)=ǫ2 ×ǫ , (1) If without considering the non-trivial mixing effect, the
0 T mix
usual electric screening masses reflecting the weak cou-
whereǫ correspondsto the twoidenticaltransverse(T) pling screening physics can be directly obtained through
T
modesandǫ tothe longitudinalmode(L)ofthe pho- M2 = ΠL(0,0) = −Π00(0,0). For example, at the em-
mix D
ton with mixing. Furthermore, one can analyze the non- pirical saturation density with Fermi-momentum kf =
∗
trivialmixingeffectsontheinter-particleEMcorrelation 256.1MeV and an effective nucleon mass M ∼ 0.8MN,
physics between the charged particles with the effective the numerical results are MP ∼43.46MeV and
D
permittivity, which is reduced to
Me =24.69MeV. (6)
D
ǫ (0,|k|→0)
eff
ThecrucialobservationisthattheThomas-Fermielec-
=1+ 1 ΠL(0,0)+ 1 (Πσ−γ,0)2 .(2) tric screening mass through the virtual (anti-)electron
k2 P m2σ+ΠσN,P P ! polarization calculation Eq.(5)-Eq.(6) instead of that
3
fromthe randomphaseapproximation(RPA)P-loopone from long range Coulomb frustration effects, the multi-
is exactly consistent with the previous estimation[11]. component baryon nucleons system can be in the novel
This scenario is also consistent with the conventional thermodynamics pasta state especially in the subsatura-
notion of plasma theory that electrons screen the long- tion nuclear density regime. The analytical exploration
range Coulomb force between protons or ions[4]. The contributes to understanding the underlying stronglyin-
either local or global charge neutralized condition is au- teractingCoulombphysicshiddeninthediverselyupdat-
tomatically ensured through the full photon propagator ing works.
calculation[18].
In turn, a natural but very uncomfortable question
may arise from above fortuitous but exact consistency III. STRONGLY CORRELATED COMPACT
Eqs.(5-6) is: Will the nucleons “screen” the EM interac- MATTER THERMODYNAMICS
tion between the opposite charged lepton electrons?
Thesystematicstudyisnon-trivialasnaivelyexpected A. Formalism
because the solutions will involve the Debye mass that
can become catastrophically imaginary. With the de- With above analysis,the isoscalarEM interactionem-
nominator in the bracket of Eq.(2), the term ΠL(0,0)+ beddedintherelativisticnucleartheoryhasthe strongly
P
(Πσ−γ,0)2/(m2 +Π ) may be smaller than ΠL(0,0) and coupling confinement characteristic which promotes us
P σ σ P
the effective permittivity can be negative due to the to construct a Proca-like Lagrangian to deal with the
isospin mixing effects of isoscalar σ and γ with the un- unusual quantum mechanical Coulomb effects between
usual sigma meson self-energy behavior Eq.(4). In deed, the charged baryon particles[11]. In this work, we at-
the Fermi-sea contribution dominates over the Dirac temptatwo-photonnon-perturbativeapproachtomodel
sea’s, i.e., the in-medium/density fluctuation effects can the thermodynamics properties of the charge neutral-
lead to the under(anti)-screening effects[16]. The nega- ized PeνN plasma with global vanishing net electric
tive permittivity implies that there is a strongly coupled charge chemical potential. The effective theory involves
characteristic EM instability in a compact environment. the interaction of Dirac nucleons and electrons with an
This Fermi surface instability results from the rummy auxiliary Maxwell-Proca like EM field as well as the
competition between the short range nuclear force at- scalar/vectormesons fields
traction and the long range EM fluctuation repulsion.
In our perception, the complete isospin mixing calcu- LQHD−σ,ω,ρ+Le;
lations for the strongly coupled nucleons is a seriously 1
L = − F Fµν;
difficult task,whichwe suspectwillrequireagreaterun- γ,free 4 µν
derstanding of nuclear force. We do not claim to have 1
a complete solution. Intuitively we can make an ansatz LI,γ−P = 2m2γ,eδµ0AµAµ+AµJPµ;
that the final analytical expression can be reduced to 1
LI,γ−e = 2m2γ,Pδµ0AµAµ+AµJeµ. (8)
ΠL(0,0)+mixing contribution=−ΠL(µ∗,T ), (7)
P e P P
Thefulldescriptionfortherelevantdegreesoffreedomin
whichcanbeinprinciplerealizedthroughotherinvolved the Lagrangian can be found in the literature[8, 11]. In
isospin mixing discussions σ−ω, γ−ω esp. the unclear Eqs.(8), the electric currents contributed by the baryon
charge symmetry breaking term ρ−ω etc. attributed to protons and lepton electrons are as follows, respectively
the different current quark masses which is beyond the
(1+τ )
scope of the adopted effective theory framework. These Jµ =−eψ¯ γµ 3 ψ , Jµ =e¯l γµl . (9)
effects can be manifested through the two-photon [19] P P 2 P e e e
approach in an easily controllable way. The two-photon
Based on the local gauge invariant free Lagrangian,
formalism as given in Sec. III will confirm this ansatz
the gauge invariant effective interaction actions can be
indirectlythroughtheThomsonstabilityconditionofthe
constructed by the standard way[20, 21], respectively
lepton electrons thermodynamics background.
With excitation concepts in plasma dielectric function 1
theory, the modes determined by the poles of the full LI =− FµνFµν +|DµH|2+V(H)+AµJµ. (10)
4
propagators may be spacelike and of tachyonic charac-
teristic which is closely related to the Landau damp- The two photon mass gaps(i.e., the Higgs charge and
ing and consistent with the nonlinear response prop- the expectation value of the Higgs background field) are
erty. From the viewpoint of isospin mixing, the EM in- free Lagrangemultiplier parameters, i.e., they should be
teractions between the point-like particles explored by determined by relevant thermodynamics identities and
the relativistic nuclear field theory are not simply/only critical dynamics constraint criterions.
screened and their contribution to thermodynamics can- Based on introducing the photon isospin concept, the
not be neglected by naively taking the ideal degenerate conventional electromagnetic current is divided into two
gas or quasi-particle picture of normal fluid. Resulting parts: one is the baryon current contribution of electric
4
charged protons; the other is the lepton current of op- C. Mass gap multiplier with Thomson stability
posite charged electrons. The position permutation of
thetwomassgapparametersinrelevanteffectiveactions The mass gap m2 is a Lagrange multiplier that en-
γ,P
Eq.(8) makes it possible to deal with the interior EM
forces relevant physical dynamics constraints. The re-
interaction as auxiliary external field approximation one maining task is how to determine this gapparameter re-
another to ensure the theoretical thermodynamics self-
flecting the quantum fluctuating effects.
consistency for the two opposite charged subsystems.
According to the general density correlation theory of
statistical physics, the following identity should be ful-
filled at the infrared singular critical point with strong
B. Thermodynamics potential of strongly coupled
fluctuation
electrons through vector condensation
∂P
e
| =0. (18)
Thecurrentconservationisguaranteedbythe Lorentz ∂ρ T
e
transversality condition with HLS formalism
Therefore the total lepton number density has to make
∂ Aµ =0, (11)
µ the system stable by minimizing the thermodynamical
whichcanbe naturallyrealizedby takingthe relativistic potential. We find that this crucial relation can be used
Hartree instantaneous approximation (RHA) formalism. to determine the unknown mass gap multiplier. Mini-
As a complementarity to the discussion for the nucle- mizingthethermodynamicalpotentialoftheleptonssys-
ons background thermodynamics[11] with the Coulomb tem(made of electrons and implicit neutrinos) stabilized
frustrating effects, we presently limit to the thermody- by the external baryon background with the mathemat-
namicsofthestronglycorrelateddiluteelectrons(lepton) ically well defined effective potential or pressure Eq.(14)
backgroundinadense andhotcompactnuclearenviron- functional with Eq.(16)[2]
ment with the following effective Lagrangian
∂Ω
Leffective = ψ¯e(iγµ∂µ+γ0µe−me)ψe ∂ρee|m2γ,P,T =0, (19)
1 1
− F Fµν + m2 A Aµ+A Jµ
4 µν 2 γ,P µ µ e one has
+δL (.12)
Auxiliary NuceonsCountertermBackground e2 3µ∗2
The A is the vector field with the field stress m2 =− (T2+ e )=−m2 , (20)
µ γ,P 3 π2 γ,e
F =∂ A −∂ A . (13)
µν µ ν ν µ
which is the negative gauge invariant electric screening
InEq.(12),me isthebareelectronmasswiththeback- mass squared obtained through the photon polarization
groundfluctuatingvectorbosonmassgapsquaredm2γ,P. Eq.(3) with the full electron propagator Eq.(17).
Intermsoffinitetemperaturefieldtheorywithfunctional With some algebra operations, it is easy to find that
path integral[8, 11, 17], the effective potential reads Eq.(19) is also equivalent to the additional global U(1)
Ωe/V = −12m2γ,PA20−2T {ln(1+e−β(Ee−µ∗e)) lepton conservation
+ln(1+eZ−kβ(Ee+µ∗e))}. (14) ∂∂Ωµee|m2γ,P,T =0. (21)
The particle(charge) number density ρ = 2 (n −n¯ )
e k e e The physical meanings of Eq.(15) and Eq.(21) are quite
is well defined by the thermodynamics identity
R different from each other. The former is thermodynam-
∂Ω
e ics relation identity, while the latter is the “mechanical”
| ≡−ρ . (15)
∂µe A0 e stability criterion. The relation between m2γ,P(µ∗P) and
The tadpole diagramwith photonself-energyfor the full m2 (µ∗) can be confirmed by comparing Eq.(16) with
γ,e e
fermion electron propagator leads to that obtained for protons A = e/m2 ρ , by noting
0 γ,e P
e ρe =ρP for the classical thermodynamics ground state.
A =− ρ , (16)
0 m2 e The Eq.(20) is similar to the relation between the De-
γ,P
bye mass and pressure for the ideal degenerate/quasi-
∗
from which the effective chemical potential µe is defined particle gas derived with Ward-Identity responsible for
with a gauge invariant manner[4] thecurrentconservation/gaugeinvariance[17]. Themag-
∗ e2 nitude of the gauge invariant ratio m2γ,(e,P)/e2 is the
µ ≡µ +µ =µ − ρ . (17)
e e e,I e m2 e density of states for symmetric two component degrees
γ,P
of freedom with spin down and up. The contribution
∗ ∗
The ne(µe,T) and ne(µe,T) are the distribution func- µe,Ito the effective chemical potential characterizes the
tionsfor(anti-)particleswithE = k2+m2. Through- long range correlation physics, which leads to the phase
e e
out this paper, we set m =0 as done in the literature. space deformation of the particle distribution functions.
e
p
5
The thermodynamics properties can be learned from can be attractive in the dilute strongly coupling limit
the underlying effective potential consequently. With with the nuclear confinement effects. This can be con-
Eq.(14) and the standard thermodynamics relation firmedfromthenegativescatteringlengthsbetweenelec-
trons obtained from the oscillatory stochastic Coulomb
1 ∂(βΩ )
ǫe = e +µeρe, (22) potentiale2cos(|mγ,P|r)/(4πr)withthelowenergyBorn
V ∂β approximation. The static Coulomb force between the
itinerant electrons is modulated by the opposite charged
the energy density functional is
nonlinear space-like baryon system, and so the electrons
ǫ = e2 ρ2+2 E [n (µ∗,T)+n¯ (µ∗,T)].(23) becomehighlyturbulentandareconfinedtosomeextent.
e 2m2 e e e e e e Likethe effectivefermionmassconcept,the contribution
γ,P Zk
µ to physical effective chemical potential character-
e,I
izes the collective effects. This effect is more obvious
D. Negative pressure contribution by rewriting µ∗e = me∗2+µ2e at T →0. Assuming the
globalchemicalpotentialµ fixed,theelectronswillbeef-
e
p
fectivelymoreheavyanalogoustotheKondophysics[22].
We analyze concretely the pressure P = −Ω /V at
e e
Especially, the physics explored is quite similar to the
T =0,
quantum Ising characteristic BEC-BCS crossover ther-
e2µ6 µ4 modynamics studied with the Feshbach resonancein the
P = e + e . (24)
e 18π4m2 12π2 oppositenon-relativisticlimit. Motivatedbytheunderly-
γ,P
inghomology[23],theanalyticaluniversalfactoriscalcu-
With Eq.(20), the pressure Eq.(24) can be reduced to latedtobeξ =(d−2)(d+1)/d2fordspatialdimensions
through this counterterm analytical method. The result
1 µ4 µ4 α
P = e = e 1−286.9 , (25) for d = 3 is exactly consistent with the Monte Carlo
e 312π2 12π2 π
study[24]. Here, the ξ is the ratioofbinding energyden-
(cid:16) (cid:17)
in order to be compared with the analytical result ex- sity in the strongly coupling unitarity limit to that for
pected by Kapusta in addressing the relevant compact the non-interacting ideal fermion gas.
objectthermodynamicssuchasforthe white dwarfstars The surprising macroscopical like-charged attraction
masscorrectionresultingfromthenovelEMinteractions phenomenacanbeattributedtothehydrodynamicback-
ofcollectiveelectrons. This non-perturbativecalculation groundeffect[25]andthesimilarpossibilityisaninterest-
can readily approach to his anticipation about a very ing topic in current cosmology etc.[12]. Here, this coun-
large negative contribution to pressure (the coefficient terintuitive quantum phenomena through an oscillating
of the α/π term in Eq.(26) could have been ∼ 102 in- potential between the collective electrons is found from
stead of 3[17]), but has no effect on the beautiful Chan- the point of view of the photon isospin mixing effects.
2
drasekhar mass limit because this contribution has been Before closing the discussion, let us stress that this
exactlycouneractedbytheoppositechargedsystemwith is the quantum many-body effect, i.e, it is the density
strongly repulsive long range correlations. correlation/fluctuationleadstoarefreshinglongdistance
What new physics can be found? Different from the quantum dragging picture. Due to the presence of finite
weak coupling perturbative resummation result[17] chemicalpotentialinadditiontothetemperatureEq.(3),
the Lorentz symmetry gets spontaneously broken in the
µ4 3α
e 1− , (26) medium which leads to the nontrivial mixing of vector
12π2 2π andscalaralthoughtherotationisstillagoodsymmetry
(cid:18) (cid:19)
by noting that the spin angular momentum is a good
the analytical result Eq.(25) does not reply on the cou-
quantum number. The nontrivial quantum transport of
pling constant α = e2/(4π). The long range quantum
the stronglycoupledelectronsresulting fromthe derived
fluctuation/correlation effects leads to the negative con-
effective attractiveopticalpotential inthe specific dilute
tribution, which is of universal characteristic. The in-
pasta phase deserves to be further studied in detail.
duced negative interaction energy between the collective
electrons can be as large as their kinetic energy and the
transport coefficients such as the shear viscosity of elec-
V. SUMMARY
trons will be reduced significantly compared with the
ideal/quasi-particle gas model although it is very hard
to say electrons are in a superconductivity state. Mathematically, this two-photon counterterm ap-
proach is analogous to the general stability principle of
the Newton’s action-reaction law in mechanics. The
IV. STRONGLY COUPLING LIMIT PHYSICS screening corresponds to action, while antiscreening to
AND DISCUSSIONS reaction. Rewriting 0 as 0 = 1m2A Aµ− 1m2A Aµ =
2 γ µ 2 γ µ
1m (µ∗,T )2A Aµ+1m (µ∗,T )2A Aµ andtaking
2 γ,e e e µ 2 γ,P P P µ
It is very interesting that the instantaneous strong a bulk system as two opposite charged interacting sub-
Coulomb interaction between the like-charged electrons systems through an external electrostatic potential con-
6
tribute to gauging/removing the infrared singularity di- for understanding the collective effects in the strongly
vergences. Theexternalsourceformalismmakesitpossi- interacting charged systems. From the pure academic
bletodealwiththeinteriorlongrangefluctuationeffects, viewpointofin-mediumisospinandspontaneousLorentz
while the perturbative Furry’s theorem limit is evaded. violation effects, the EM photon’s role deserves to be
In spirit, this approach is similar to the multi-grand further explored because “More is different” as said by
canonicalensemblestaticalphysics,whichguaranteesthe P.W. Anderson[22]. This provides a practicable coun-
physicalconstraintconditions,i.e., the gauge invariance, tertermcompensatoryschemetodetectandgaugethein-
unitarity and the thermodynamics self-consistency. fraredEMinstabilityinadilutestronglycouplingsystem
Inconclusion,wehaveanalyzedtheisospinmixingdue with either vanishing or nonvanishing net global electric
to photon in the relativistic nuclear theory and take a charge chemical potential. The author acknowledges the
two-photonmethodwithHLSformalismtoapproachthe discussions with Profs. Bao-an Li, Jia-rong Li, Hong-
strongly correlated charged multi-components fermion an Peng, Fan Wang and Lu Yu. He is also grateful to
thermodynamics by taking the mysterious protons, elec- the beneficial communications with Profs. Ling-Fong Li
trons and photons as an example. The instantaneous and J. Piekawewicz. Supported in part by the start-
RHA approximation and RPA techniques capture many ing research fund of CCNU and NSFC under grant No
ofthe non-trivialemergentphenomena whicharecrucial 10675052. Initialedwiththereferees’suggestionsfor[11].
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