Fermion Propagator Research Articles

Manifestly gauge-covariant representation of scalar and fermion propagators

A new way to write the massive scalar and fermion propagators on a background of a weak gauge field is presented. They are written in a form that is manifestly gauge-covariant up to several additional terms that can be written as boundary terms in momentum space. These additional terms violate Ward-Takahashi identities and need to be renormalized by appropriate counterterms if the complete theory is to be gauge-covariant. This form makes it possible to calculate many amplitudes in a manifestly gauge-covariant way (at the same time reducing the number of Feynman diagrams). It also allows to express some counterterms in a way independent of the regularization scheme and provides an easy way to derive the anomalous term affecting the chiral current conservation.

Chiral phase transition inQED3at finite temperature and impurity potential

In a realistic interacting system described by ($2+1$)-dimensional quantum electrodynamics (${\mathrm{QED}}_{3}$), there is always a certain number of impurities by which fermions are scattered. In general, impurity scattering can generate a finite density of states at the Fermi level, which screens the temporal component of the gauge field. This effect is expected to weaken dynamical fermion mass generation. Within the Born approximation, by introducing a damping term in the energy component of the fermion propagator, the influences of finite temperature and impurity scattering on the chiral phase transition in ${\mathrm{QED}}_{3}$ are investigated. Pursuing this aim, we solve the Dyson-Schwinger equations for the fermion and boson propagators to the leading order in $1/{N}_{f}$ expansion at zero frequency and then calculate the chiral condensate, the chiral susceptibility, and the thermal susceptibility within a range of the impurity scattering rates $\mathrm{\ensuremath{\Gamma}}$ and the numbers of fermion flavors ${N}_{f}$. It is found that impurity scattering leads to an obvious suppression of the dynamical fermion mass generation and critical temperature ${T}_{c}$.

Pseudoscalar Fields in Torsionful Geometries of the Early Universe, the Baryon Asymmetry and Majorana Neutrino Mass Generation

We discuss here a specific field-theory model, inspired from string theory, in which the generation of a matter-antimatter asymmetry in the Cosmos is due to the propagation of fermions in a non-trivial, spherically asymmetric (and hence Lorentz violating) gravitational background that may characterise the epochs of the early universe. The background induces different dispersion relations, hence populations, between fermions and antifermions, and thus CPT Violation (CPTV) already in thermal equilibrium. Species populations may freeze out leading to leptogenesis and baryogenesis. More specifically, after reviewing some generic models of background-induced CPTV in early epochs of the Universe, we consider a string- inspired scenario, in which the CPTV is associated with a cosmological background with torsion provided by the Kalb-Ramond (KR) antisymemtric tensor field of the string gravitational multiplet. In a four-dimensional space time this field is dual to a pseudoscalar “axion-like” field. The thermalising processes in this model are (right-handed) Majorana neutrino-antineutrino oscillations, which are induced in the presence of the KR axion background. These processes freeze out at a (high) temperature Tc ≫ m, where m is the Majorana neutrino mass, at which the KR background goes to zero or is diminished significantly, through appropriate phase transitions of the (string) universe. An additional, but equally important, role, of the KR field is that its quantum fluctuations and mixing with an ordinary axion, which couples to the Majorana neutrinos via appropriate Yukawa couplings, can also lead to the generation of a Majorana neutrino mass through quantum anomalies. This provides a novel way for generating neutrino masses, independent of the traditional seesaw mechanism.

Método de Ritus para o cálculo do propagador de Feynman

Neste artigo vamos resgatar a sensasional ideia devida a V. Ritus para o cálculo do propagador de Feynman. Faremos uma discussão geral do método e o aplicaremos ao cálculo do propagador de um campo bosônico e fermiônico sujeitos a um campo magnético não quantizado constante e homogêneo.

Phase of the fermion determinant inQED3using a gauge invariant lattice regularization

We use canonical formalism to study the fermion determinant in different three dimensional abelian gauge field backgrounds that contain non-zero magnetic and electric flux in order to understand the non-perturbative contributions to the parity-odd and parity-even parts of the phase. We show that a certain phase associated with free fermion propagation along a closed path in a momentum torus is responsible for the parity anomaly in a background with non-zero electric flux. We consider perturbations around backgrounds with non-zero magnetic flux to understand the structure of the parity-breaking perturbative term at finite temperature and mass.

Fermion masses without symmetry breaking in two spacetime dimensions

I study the prospect of generating mass for symmetry-protected fermions without breaking the symmetry that forbids quadratic mass terms in the Lagrangian. I focus on 1+1 spacetime dimensions in the hope that this can provide guidance for interacting fermions in 3+1 dimensions. I first review the SO(8) Gross-Neveu model and emphasize a subtlety in the triality transformation. Then I focus on the "m = 0" manifold of the SO(7) Kitaev-Fidkowski model. I argue that this theory exhibits a phenomenon similar to "parity doubling" in hadronic physics, and this leads to the conclusion that the fermion propagator vanishes when p = 0. I also briefly explore a connection between this model and the two-channel, single-impurity Kondo effect. This paper may serve as an introduction to topological superconductors for high energy theorists, and perhaps as a taste of elementary particle physics for condensed matter theorists.

Fermionic propagator in an intense background

New results for the fermion propagator in a laser background are presented. We show that the all orders electron propagator can be written in a compact and appealing form as a sum of sideband poles with a matrix wave function renormalisation and a matrix valued mass shift. This last result is essential in the fermionic theory if we are to maintain that both the mass and its square pick up a correction only at order e^2. A perturbative verification of our results is carried out.

Classical-physics applications for Finsler b space

The classical propagation of certain Lorentz-violating fermions is known to be governed by geodesics of a four-dimensional pseudo-Finsler b space parametrized by a prescribed background covector field. This work identifies systems in classical physics that are governed by the three-dimensional version of Finsler b space and constructs a geodesic for a sample non-constant choice for the background covector. The existence of these classical analogues demonstrates that Finsler b spaces possess applications in conventional physics, which may yield insight into the propagation of SME fermions on curved manifolds.

High-order path-integral Monte Carlo methods for solving quantum dot problems.

The conventional second-order path-integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of antisymmetric free-fermion propagators that are needed to extract the ground state wave function at large imaginary time. In this work we show that optimized fourth-order path-integral Monte Carlo methods, which use no more than five free-fermion propagators, can yield accurate quantum dot energies for up to 20 polarized electrons with the use of the Hamiltonian energy estimator.

Dynamical chiral symmetry breaking in the NJL model with a constant external magnetic field

In this paper, we develop a new method that is different from the Schwinger proper time method to deduce the fermion propagator with a constant external magnetic field. In the NJL model, we use this method to find the gap equation at zero and nonzero temperature and give the numerical results and phase diagram between the magnetic field and temperature. Additionally, we introduce the current mass to study the susceptibilities because there is a new parameter (the strength of the external magnetic field) in this problem. Corresponding to this new parameter, we define a new susceptibility ${\ensuremath{\chi}}_{B}$ to compare with the other two susceptibilities ${\ensuremath{\chi}}_{c}$ (chiral susceptibility) and ${\ensuremath{\chi}}_{T}$ (thermal susceptibility). All three susceptibilities show that when the current mass is not zero, the phase transition is a crossover, while for comparison, in the chiral limit, the susceptibilities show a second order phase transition. Last, we give the critical coefficients of different susceptibilities in the chiral limit.

3D field theories with Chern-Simons term for large N in the Weyl gauge

Three dimensional, $U(N)$ symmetric, field theory with fermion matter coupled to a topological Chern--Simons term, in the large $N$ limit is analyzed in details. We determine the conditions for the existence of a massless conformal invariant ground state as well as the conditions for a massive phase. We analyze the phase structure and calculate gauge invariant corelators comparing them in several cases to existing results. In addition to the non-critical explicitly broken scale invariance massive case we consider also a massive ground state where the scale symmetry is spontaneously broken. We show that such a phase appears only in the presence of a marginal deformation that is introduced by adding a certain scalar auxiliary field and discuss the fermion-boson dual mapping. The ground state contains in this case a massless $U(N)$ singlet bound state goldstone boson- the dilaton whose properties are determined. We employ here the temporal gauge which is at variance with respect to past calculations using the light-cone gauge and thus, a check (though limited) of gauge independence is at hand. The large $N$ properties are determined by using a field integral formalism and the steepest descent method. The saddle point equations, which take here the form of integral equations for non-local fields, determine the mass gap and the dressed fermion propagator. Vertex functions are calculated at leading order in $1/N$ as exact solutions of integral equations. From the vertex functions, we infer gauge invariant two-point correlation functions for scalar operators and a current. Indications about the consistency of the method are obtained by verifying that gauge-invariant quantities have a natural $O(3)$ covariant form. As a further verification, in several occasions, a few terms of the perturbative expansion are calculated and compared with the exact results in the appropriate order.

Schwinger–Dyson equation and NJL approximation in massive gauge theory with fermions

We consider massive SU(N) gauge theory with fermions. Gauge bosons become massive due to the interaction with the scalar field, whose vacuum average provides the spontaneous breakdown of gauge symmetry. We investigate Dyson–Schwinger equation for the fermion propagator written in ladder approximation and in Landau gauge. Our analysis demonstrates that the chiral symmetry breaking in the considered theory is the strong coupling phenomenon. There are the indications that there appears the second order phase transition between chirally broken and symmetric phases of the theory at the value of coupling constant αc=(1+γ)×π3×12C2(F), where 0<γ<1, and γ depends on the scale, at which the fluctuations of the scalar field destroy the gauge boson mass. In the broken phase near the critical value of α the Dyson–Schwinger equation is approximated well by the gap equation of the effective Nambu–Jona-Lasinio model with the value of cutoff around gauge boson mass M and the effective four-fermion coupling constant 4παM2×2C2(F)N. The dynamical fermion mass m may be essentially smaller than M.

Different critical points of chiral and deconfinement phase transitions in (2 + 1)-dimensional fermion–gauge interacting model

Based on the truncated Dyson-Schwinger equations for fermion and massive boson propagators in QED(3), the fermion chiral condensate and the mass singularities of the fermion propagator via the Schwinger function are investigated. It is shown that the critical point of the chiral phase transition is apparently different from that of the deconfinement phase transition and in Nambu phase the fermion is confined only for small gauge-boson mass.

Zero Mode Effect Generalization for the Electromagnetic Current in the Light Front: Fermion Case

We investigate the effect of the γ+ term in the fermion propagator on the zero mode in a system composed of two free fermions propagating in a background field. For this purpose we use the technique of global propagators in the light front and current operator in order to obtain the electromagnetic current component J−.

Influence of gauge boson mass on the staggered spin susceptibility

Based on the study of the linear response of the fermion propagator in the presence of an external scalar field, we calculate the staggered spin susceptibility in the low-energy limit in the framework of the Dyson-Schwinger approach. We analyze the effect of a finite gauge boson mass on the staggered spin susceptibility in both the Nambu phase and the Wigner phase. It is found that the gauge boson mass suppresses the staggered spin susceptibility in the Wigner phase. In addition, we try to give an explanation for why the antiferromagnetic spin correlation increases when the doping is lowered.

The Epstein–Glaser causal approach to the light-front QED4. II: Vacuum polarization tensor

In this work we show how to construct the one-loop vacuum polarization for light-front QED4 in the framework of the perturbative causal theory. Usually, in the canonical approach, it is considered for the fermionic propagator the so-called instantaneous term, but it is known in the literature that this term is controversial because it can be omitted by computational reasons; for instance, by compensation or vanishing by dimensional regularization. In this work we propose a solution to this paradox. First, in the Epstein–Glaser causal theory, it is shown that the fermionic propagator does not have instantaneous term, and with this propagator we calculate the one-loop vacuum polarization, from this calculation it follows the same result as those obtained by the standard approach, but without reclaiming any extra assumptions. Moreover, since the perturbative causal theory is defined in the distributional framework, we can also show the reason behind our obtaining the same result whether we consider or not the instantaneous fermionic propagator term.

Sizable electron/neutron electric dipole moment inD3/D7μ-split supersymmetry

Within the framework of $\mathcal{N}=1$ gauged supergravity, using a phenomenological model that can be obtained locally as a Swiss-cheese Calabi-Yau string-theoretic compactification with a mobile $D3$-brane localized on a nearly special Lagrangian three cycle in the Calabi-Yau and fluxed stacks of wrapped $D7$-branes, and which provides a natural realization of $\ensuremath{\mu}$-split supersymmetry (SUSY), we show that in addition to getting a significant value of an [electron/neutron (e/n)] electron dipole moment (EDM) at two-loop level, one can obtain a sizable contribution of (e/n) EDM even at one-loop level due to the presence of heavy supersymmetric fermions nearly isospectral with heavy sfermions. Unlike traditional split SUSY models in which the one-loop diagrams do not give significant contribution to the EDM of the electron/neutron because of very heavy sfermions existing as propagators in the loop, we show that one obtains a ``healthy'' value of the EDM in our model because of the presence of a heavy Higgsino, neutralino/chargino, and gaugino as fermionic propagators in the loops. The independent $CP$-violating phases are generated from nontrivial distinct phase factors associated with four Wilson line moduli [identified with first-generation leptons and quarks and their $SU(2{)}_{L}$-singlet cousins] as well as the $D3$-brane position moduli (identified with two Higgses), and the same are sufficient to produce overall distinct phase factors corresponding to all possible effective Yukawas as well as effective gauge couplings that we discuss in the context of $\mathcal{N}=1$ gauged supergravity action. However, the complex phases responsible to generate a nonzero EDM at one-loop level mainly appear from an off-diagonal contribution of sfermion as well as Higgs mass matrices at the electroweak scale (EW). In our analysis, we obtain a dominant contribution of the electron/neutron EDM around ${d}_{e}/e\ensuremath{\equiv}\mathcal{O}(1{0}^{\ensuremath{-}29})\text{ }\text{ }\mathrm{cm}$ from two-loop diagrams involving heavy sfermions and a light Higgs, and ${d}_{e}/e\ensuremath{\equiv}\mathcal{O}(1{0}^{\ensuremath{-}32})\text{ }\text{ }\mathrm{cm}$ from a one-loop diagram involving a heavy chargino and a light Higgs as propagators in the loop. The neutron EDM gets a dominant contribution of the order ${d}_{n}/e\ensuremath{\equiv}\mathcal{O}(1{0}^{\ensuremath{-}33})\text{ }\text{ }\mathrm{cm}$ from the one-loop diagram involving SM-like quarks and Higgs. To justify the possibility of obtaining a large EDM value in the case of a Barr-Zee diagram which involves ${W}^{\ifmmode\pm\else\textpm\fi{}}$ and the Higgs (responsible to generate the nontrivial $CP$-violating phase) in the two-loop diagrams as discussed by Leigh et al. [Nucl. Phys. B267, 509 (1986)], we provide an analysis of the same in the context of our $D3/D7$ $\ensuremath{\mu}$-split SUSY model at the EW scale. By conjecturing that the $CP$-violating phase can appear from the diagonalization of the Higgs mass matrix obtained in the context of $\ensuremath{\mu}$-split SUSY, we also get an EDM of the electron/neutron around $\mathcal{O}(1{0}^{\ensuremath{-}27})\text{ }\text{ }e\text{ }\mathrm{cm}$ in the case of the two-loop diagram involving ${W}^{\ifmmode\pm\else\textpm\fi{}}$ bosons.

Determine the critical fermion flavor in three-dimensional QED using nonlocal gauge

We determine the critical fermion flavor for dynamical chiral symmetry breaking in three-dimensional quantum electrodynamics using nonlocal gauge (gauge parameter depends on the momentum or coordinate). The coupled Dyson–Schwinger equations of the fermion and gauge boson propagators are considered in the vicinity of the critical point. Illustrated by using the transverse vertex proposed by Bashir et al., we show that: for a variety of the transverse vertex, the critical flavor is still 128/3π2, the same as using the bare vertex.

Quantum field theoretic properties of Lorentz-violating operators of nonrenormalizable dimension in the fermion sector

In the current paper the properties of a quantum field theory based on certain sets of Lorentz-violating coefficients in the nonminimal fermion sector of the Standard Model extension are analyzed. In particular, three families of coefficients are considered, where two of them are $CPT$ even and the third is $CPT$ odd. As a first step the modified fermion dispersion relations are obtained. Then the positive- and negative-energy solutions of the modified Dirac equation and the fermion propagator are derived. These are used to demonstrate the validity of the optical theorem at tree level, which provides a cross-check for the results obtained. Furthermore unitarity is examined and seems to be valid for the first set of $CPT$-even coefficients. However for the remaining sets certain issues with unitarity are found. The article demonstrates that the adapted quantum field theoretical methods at tree level work for the nonminimal, Lorentz-violating framework considered. Besides, the quantum field theory based on the first family of $CPT$-even coefficients is most likely well behaved at lowest order perturbation theory. The results are important for future phenomenological investigations carried out in the context of field theory, e.g., the computation of decay rates and cross sections at tree level.

The semiclassical propagator in fermionic Fock space

We present a rigorous derivation of a semiclassical propagator for anticommuting (fermionic) degrees of freedom, starting from an exact representation in terms of Grassmann variables. As a key feature of our approach the anticommuting variables are integrated out exactly, and an exact path integral representation of the fermionic propagator in terms of commuting variables is constructed. Since our approach is not based on auxiliary (Hubbard-Stratonovich) fields, it surpasses the calculation of fermionic determinants yielding a standard form $\int {\cal D}[\psi,\psi^{*}] {\rm e}^{i R[\psi,\psi^{*}]}$ with real actions for the propagator. These two features allow us to provide a rigorous definition of the classical limit of interacting fermionic fields and therefore to achieve the long-standing goal of a theoretically sound construction of a semiclassical van Vleck-Gutzwiller propagator in fermionic Fock space. As an application, we use our propagator to investigate how the different universality classes (orthogonal, unitary and symplectic) affect generic many-body interference effects in the transition probabilities between Fock states of interacting fermionic systems.