On the consistency of Lorentz invariance violation in QED induced by fermions in constant axial-vector background

We show for the first time that the induced parity-even Lorentz invariance violation can be unambiguously calculated in the physically justified and minimally broken, dimensional regularization scheme, suitably tailored for a spontaneous Lorentz symmetry breaking in a field theory model. The quantization of the Lorentz invariance violating quantum electrodynamics is critically examined and shown to be consistent either for a light-like cosmic anisotropy axial-vector or for a time-like one, when in the presence of a bare photon mass.     

Aspects of UA (1) breaking in the Nambu and Jona-Lasinio model

The six-quark instanton induced ’t Hooft interaction, which breaks the unwanted U_A (1) symmetry of QCD, is a source of perturbative corrections to the leading order result formed by the four-quark forces with the U_L (3) × U_R (3) chiral symmetry. A detailed quantitative calculation is carried out to bosonize the model by the functional integral method. We concentrate our efforts on finding ways to integrate out the auxiliary bosonic variables. The functional integral over these variables cannot be evaluated exactly. We show that the modified stationary phase approach leads to a resummation within the perturbative series and calculate the integral in the “two-loop” approximation. The result is a correction to the effective mesonic Lagrangian which may be important for the low-energy spectrum and dynamics of the scalar and pseudoscalar nonets.     

Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons

The combined effective low energy QCD Lagrangians of Nambu-Jona-Lasinio (NJL) and ’t Hooft are supplemented with eight-quark interactions. This work is a follow-up of recent findings, namely (i) the six quark flavour determinant ’t Hooft term destabilizes the NJL vacuum, (ii) the addition of a chiral invariant eight-fermion contact term renders the ground state of the theory globally stable; (iii) stability constrains the values of coupling constants of the model, meaning that even in the presence of eight-quark forces the system can be unstable in a certain parameter region. In the present work we study a phenomenological output of eight-quark interactions considering the mass spectra of pseudoscalar and scalar mesons. Mixing angles are obtained and their equivalence to the two angle approach is derived. We show that the masses of pseudoscalars are almost neutral to the eight-quark forces. The only marked effect of the second order in the SU(3) breaking is found in the η-η′ system. The scalars are more sensitive to the eight-quark interactions. A strong repulsion between the singlet and octet members is the reason for the obtained low mass of the σ state within the model considered.     

The radial problem in gauge field theory models

The study of spontaneous symmetry breaking patterns in theories in which the ground state is determined by the minima of a potential invariant under the symmetry group of the system may be traced back to the solution of two classes of problems, that we shall quote in Tolédano and Dmitriev’s suggestive words [P. Tolédano, V. Dmitriev, Reconstructive Phase Transitions in Crystals and Quasicrystals, World Scientific, Singapore, 1996] as angular and radial problem, respectively. Whilst the former problem, i.e., the determination of the isotropy-type stratification, has been extensively treated both in condensed matter physics and in particle physics, the radial problem, in particular the construction of the phenomenological potential allowing the realization of all the symmetry allowed symmetry phases, has up to now substantially been disregarded in gauge field theory, because renormalizability limits to four the degree of the Higgs potential and it is widely thought that spontaneous radiative mass generation can anyway fix the issue. Through a rigorous analysis in the framework of geometric invariant theory (-matrix approach) we review these facts, focussing our attention on the role of radiative corrections. Then, we propose a way of reconciling renormalizability requirement and tree-level observability of all the phases allowed by the symmetry. The idea will be illustrated in simple extensions of two-Higgs-doublet SM, with additional scalar singlets and discrete symmetries. This will allow us to explain the rationale behind all the extensions of the Higgs sectors so far proposed to generate the observed Baryon asymmetry of our Universe at the EW Phase Transition.     

Critical endpoint in the Polyakov-loop extended NJL model

The critical endpoint (CEP) and the phase structure are studied in the Polyakov-loop extended Nambu–Jona-Lasinio model in which the scalar type eight-quark (σ⁴${\sigma }^4$) interaction and the vector type four-quark interaction are newly added. The σ⁴${\sigma }^4$ interaction largely shifts the CEP toward higher temperature and lower chemical potential, while the vector type interaction does oppositely. At zero chemical potential, the σ⁴${\sigma }^4$ interaction moves the pseudo-critical temperature of the chiral phase transition to the vicinity of that of the deconfinement phase transition.     

Clebsch-Gordan coefficients for the extended quantum-mechanical Poincaré group and angular correlations of decay products

This paper describes Clebsch-Gordan coefficients (CGCs) for unitary irreducible representations (UIRs) of the extended quantum-mechanical Poincaré group . ‘Extended’ refers to the extension of the 10 parameter Lie group that is the Poincaré group by the discrete symmetries C, P, and T; ‘quantum mechanical’ refers to the fact that we consider projective representations of the group. The particular set of CGCs presented here is applicable to the problem of the reduction of the direct product of two massive, unitary irreducible representations (UIRs) of with positive energy to irreducible components. Of the 16 inequivalent representations of the discrete symmetries, the two standard representations with U_CU_P = ±1 are considered. Also included in the analysis are additive internal quantum numbers specifying the superselection sector. As an example, these CGCs are applied to the decay process of the ? (4S) meson.     

Induced Chern-Simons term of a paired electron state in the quantum Hall system

The induced Chern-Simons term for a paired electron state is calculated in the quantum Hall system by using a field theory on the von Neumann lattice. The coefficient of the Chern-Simons term, which is the Hall conductance, has not only the usual term proportional to a filling factor due to P (parity) & T (time reversal) symmetry breaking but also correction terms due to P & T & U(1) symmetry breaking. The correction term essentially comes from the Nambu-Goldstone mode and depends on an infrared limit. It is shown that the correction term is related to a topological number of a gap function in the momentum space.     

含Chern-Simons项的标量电动力学的BFV量子化

应用BFV路径积分量子化方案,给出含Chern-Simons项的标量电动力学的量子化,得到了量子系统守恒的能量、动量和角动量,指出在量子水平上系统具有分数自旋性质.     

Emission and absorption of photons and the black-body spectrum in Lorentz-odd electrodynamics

We study emission and absorption of radiation by non-relativistic electrons within the framework of a Lorentz-breaking electrodynamics in (3+1)$(3+1)$ dimensions. We have realised that Planck-type law acquires extra terms proportional to the violating parameters: For the CPT-odd model, the leading extra terms appear to be linear or quadratic in these violating parameters according to the background vector is parallel or perpendicular to the photon wave-vector. In the CPT-even case a linear correction shows up. Besides these deviations in the black-body spectra, those violations may be also probed through a difference in the photon mean occupation number for the two modes. Our results also indicate that such violations are better probed at very low temperatures, where their effects on the thermal spectra are largely enhanced.     

The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement

The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector, we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chiral symmetry is broken, either dynamically or explicitly, the running coupling is infrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex Dyson-Schwinger equation are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark-quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry. Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore, we conclude that chiral symmetry breaking and confinement are closely related. Furthermore, we discuss aspects of confinement as the absence of long-range van der Waals forces and Casimir scaling. An examination of experimental data for quarkonia provides further evidence for the viability of the presented mechanism for quark confinement in the Landau gauge.     

Alternative quantization of the Hamiltonian in loop quantum cosmology

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities. In this Letter, we quantize the Lorentz term of the gravitational Hamiltonian constraint in the spatially flat FRW model by two approaches different from that of the Euclidean term. One of the approaches is very similar to the treatment of the Lorentz part of Hamiltonian in loop quantum gravity and hence inherits more features from the full theory. Two symmetric Hamiltonian constraint operators are constructed respectively in the improved scheme. Both of them are shown to have the correct classical limit by the semiclassical analysis. In the loop quantum cosmological model with a massless scalar field, the effective Hamiltonians and Friedmann equations are derived. It turns out that the classical big bang is again replaced by a quantum bounce in both cases. Moreover, there are still great possibilities for the expanding universe to recollapse due to the quantum gravity effect.     

The anomaly cancellation mechanism in N=1, D=4 supergravity and distorted supergravity algebra with Chern-Simon forms

A mechanism is exhibited which ensures that N=1, D=4 new minimal supergravity is free of Lorentz×U(1) anomalies, for any coupling to matter, although it contains an abelian chiral gauge field. This is achieved through the determination of a new supergravity algebra characterized by the presence of a U(1)×Lorentz Chern-Simon form in the field strength of a two-form gauge field. Our analysis provides therefore an example in which Chern-Simon type interactions do occur, while preserving local supersymmetry.     

Gravitational anomaly and Hawking radiation of apparent horizon in FRW universe

Motivated by the successful applications of the anomaly cancellation method to derive Hawking radiation from various types of black hole spacetimes, we further extend the gravitational anomaly method to investigate the Hawking radiation from the apparent horizon of a FRW universe by assuming that the gravitational anomaly also exists near the apparent horizon of the FRW universe. The result shows that the radiation flux from the apparent horizon of the FRW universe measured by a Kodama observer is just the pure thermal flux. The result presented here will further confirm the thermal properties of the apparent horizon in a FRW universe.     

Stationary solutions for the parity-even sector of the CPT-even and Lorentz-covariance-violating term of the standard model extension

In this work, we focus on some properties of the parity-even sector of the CPT-even electrodynamics of the standard model extension. We analyze how the six non-birefringent terms belonging to this sector modify the static and stationary classical solutions of the usual Maxwell theory. We observe that the parity-even terms do not couple the electric and magnetic sectors (at least in the stationary regime). The Green’s method is used to obtain solutions for the field strengths E and B at first order in the Lorentz-covariance-violating parameters. Explicit solutions are attained for point-like and spatially extended sources, for which a dipolar expansion is achieved. Finally, an Earth-based experiment is presented that can lead (in principle) to an upper bound on the anisotropic coefficients as stringent as