Field Theoretical Point Of View Research Articles

Non-perturbative field theoretical aspects of graphene and related systems

In this article, we review the dynamics of charge carriers in graphene and related 2D systems from a quantum field theoretical point of view. By allowing the electromagnetic fields to propagate throughout space and constraining fermions to move on a 2D manifold, the effective theory of such systems becomes a non-local version of quantum electrodynamics (QED) dubbed in literature pseudo or reduced QED. We review some aspects of the theory assuming the coupling arbitrary in strength. In particular, we focus on the chiral symmetry breaking scenarios and the analytical structure of the fermion propagator in vacuum and under the influence of external agents like a heat bath, in the presence of a Chern-Simons term, anisotropy and in curved space. We briefly discuss the major advances and some new results on this field.

Quantum noise and vacuum fluctuations in balanced homodyne detections through ideal multi-mode detectors

Abstract The balanced homodyne detection as a readout scheme of gravitational-wave detectors is carefully examined from the quantum field theoretical point of view. The readout scheme in gravitational-wave detectors specifies the directly measured quantum operator in the detection. This specification is necessary when we apply the recently developed quantum measurement theory to gravitational-wave detections. We examine the two models of measurement. One is the model in which the directly measured quantum operator at the photodetector is Glauber’s photon number operator, and the other is the model in which the power operator of the optical field is directly measured. These two are regarded as ideal models of photodetectors. We first show these two models yield the same expectation value of the measurement. Since there is consensus in the gravitational-wave community that vacuum fluctuations contribute to the noises in the detectors, we also clarify the contributions of vacuum fluctuations to the quantum noise spectral density without using the two-photon formulation which is used in the gravitational-wave community. We found that the conventional noise spectral density in the two-photon formulation includes vacuum fluctuations from the main interferometer but does not include those from the local oscillator. Although the contribution of vacuum fluctuations from the local oscillator theoretically yields the difference between the above two models in the noise spectral densities, this difference is negligible in realistic situations.

Generalization of the Einstein coefficients and rate equations under the quantum Rabi oscillation

We have generalized Einstein coefficients and rate equations from quantum field theoretic point of view by bringing the fundamental processes and the quantum Rabi oscillation in a single footing for the light–matter interactions for nonzero Rabi frequency. We have analytically obtained multimode Jaynes–Cummings model results for the quantum Rabi oscillation of a two-level system in a lossy resonant cavity containing (i) thermal photons and (ii) injected photons of a coherent field. We have renormalized the coupling constant for the light–matter interactions for these cases. Our results match well with the seminal experimental data obtained in this regard by Brune et al (1996 Phys. Rev. Lett. 76 1800). We also have studied the population dynamics in this regard by applying the generalized Einstein rate equations.

Field theory of monochromatic optical beams: II. Classical and quantum paraxial fields

This work is the second part of an investigation aiming at the study of optical wave equations from a field-theoretic point of view. Here, we study classical and quantum aspects of scalar fields satisfying the paraxial wave equation. First, we determine conservation laws for energy, linear and angular momentum of paraxial fields in a classical context. Then, we proceed with the quantization of the field. Finally, we compare our result with the traditional ones.

Field theory of monochromatic optical beams: I. Classical fields

We study monochromatic, scalar solutions of the Helmholtz and paraxial wave equations (PWEs) from a field-theoretic point of view. We introduce appropriate time-independent Lagrangian densities for which the Euler–Lagrange equations reproduces either Helmholtz and PWEs with the z-coordinate, associated with the main direction of propagation of the fields, playing the same role of time in standard Lagrangian theory. For both Helmholtz and paraxial scalar fields, we calculate the canonical energy-momentum tensor and determine the continuity equations relating ‘energy’ and ‘momentum’ of the fields. Eventually, the reduction of the Helmholtz wave equation to a useful first-order Dirac form, is presented. This work sheds some light on the intriguing and not so acknowledged connections between angular spectrum representation of optical wavefields, cosmological models and physics of black holes.

Correspondence of cosmology from non-extensive thermodynamics with fluids of generalized equation of state

We show that there is a correspondence between cosmology from non-extensive thermodynamics and cosmology with fluids of redefined and generalized equation of state. We first establish the correspondence in the case of basic non-extensive thermodynamics, and then we proceed by investigating the more consistent case, from the quantum field theoretical point of view, of varying exponent, namely depending on the scale. The obtained duality provides a way of explaining the complicated phenomenological forms of the effective fluid equation-of-state parameters that are being broadly used in the literature, since their microphysical origin may indeed lie in the non-extensive thermodynamics of spacetime. Finally, concerning the cosmological behavior, we show that at late times the effective fluid may drive the universe acceleration even in the absence of an explicit cosmological constant, and even if the initial fluid is the standard dust matter one. Similarly, at early times we obtain an effective cosmological constant which is enhanced through screening, and hence it can drive a successful inflation without spoiling the correct late-time acceleration.

Quantized Massive Gauge Fields and Anomalous Angle-resolved Photoemission Spectra in High-Tc Cuprates

We have argued the anomalous spectra of angle-resolved photoemission of high-Tc cuprates, using quantized massive collective-gauge fields, from the field-theoretical point of view. The relation between the bosonic function of electric origin and the quantized massive collective-gauge fields has been discussed.

Massive deformations of rank-2 symmetric tensor theory (a.k.a. BRS characterization of Fierz–Pauli massive gravity)

In this paper we consider the issue of massive gravity from a pure field theoretical point of view, as the massive deformation of the gauge theory for a symmetric rank-2 tensor field. We look for the most general massive theory with well defined propagators, imposing the absence of unphysical poles. We find several possibilities, depending on the choice of the gauge fixing term. Amongst these, two solutions with good massless limit are found. The request of the absence of tachyons, alone, does not isolate the Fierz–Pauli case: several examples of massive theories, which may or may not include the Fierz–Pauli mass term, are given. On the other hand, the Fierz–Pauli theory can be uniquely identified by means of a symmetry: it turns out the the Fierz–Pauli massive gravity is the only element of the cohomology of a BRS operator.

Complete cosmic scenario from inflation to late time acceleration: Nonequilibrium thermodynamics in the context of particle creation

The paper deals with the mechanism of particle creation in the framework of irreversible thermodynamics. The second order non-equilibrium thermodynamical prescription of Israel and Stewart has been presented with particle creation rate, treated as the dissipative effect. In the background of a flat FRW model, we assume the non-equilibrium thermodynamical process to be isentropic so that the entropy per particle does not change and consequently the dissipative pressure can be expressed linearly in terms of the particle creation rate. Here the dissipative pressure behaves as a dynamical variable having a non-linear inhomogeneous evolution equation and the entropy flow vector satisfies the second law of thermodynamics. Further, using the Friedmann equations and by proper choice of the particle creation rate as a function of the Hubble parameter, it is possible to show (separately) a transition from the inflationary phase to the radiation era and also from matter dominated era to late time acceleration. Also, in analogy to analytic continuation, it is possible to show a continuous cosmic evolution from inflation to late time acceleration by adjusting the parameters. It is found that in the de Sitter phase, the comoving entropy increases exponentially with time, keeping entropy per particle unchanged. Subsequently, the above cosmological scenarios has been described from field theoretic point of view by introducing a scalar field having self interacting potential. Finally, we make an attempt to show the cosmological phenomenon of particle creation as Hawking radiation, particularly during the inflationary era.

Inhomogeneous phases in one-dimensional mass- and spin-imbalanced Fermi gases

We study the phase diagram of strongly interacting fermions in one dimension at finite temperature, with mass and spin imbalance. By including the possibility of the existence of a spatially inhomogeneous ground state, we find regions where spatially varying superfluid phases are favored over homogeneous phases. We obtain estimates for critical values of the temperature, mass, and spin imbalance, above which these phases disappear. Finally, we show that an intriguing relation exists between the general structure of the phase diagram and the binding energies of the underlying two-body bound-state problem. Although our present study of the many-body aspects is based on a mean-field approximation, it may still yield phenomenologically important insights into the dynamics of strongly interacting fermions in one dimension. Most importantly, however, we expect that our present mean-field study can be considered worthwhile from a field-theoretical point of view as it may help to better understand the mechanisms underlying the emergence of inhomogeneous phases in higher dimensions as well as the general structure of the associated phase diagrams.

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

In the context of the nonminimal Standard Model extension a special subset of the $CPT$-even higher-dimensional operators in the photon sector is discussed from a quantum field theoretical point of view. The modified dispersion laws, photon polarization vectors and the gauge field propagator are obtained and their properties are analyzed. It is demonstrated that for certain sectors of the modified theory a puzzle arises for the optical theorem at tree level. This is followed by a discussion of how it can be interpreted and resolved at first order Lorentz violation. Furthermore the commutator of two gauge fields that are evaluated at different spacetime points is obtained and discussed. The structure of the theory is shown to resemble the structure of the modification based on the corresponding dimension-4 operator. However some properties are altered due to the nonrenormalizable nature of the theory considered. The results provide more insight into the characteristics of Lorentz-violating quantum field theories that rest upon contributions of nonrenormalizable dimension.

Gravitational Field Equations and Theory of Dark Matter and Dark Energy

The main objective of this article is to derive new gravitational field equations and to establish a unified theory for dark energy and dark matter. The gravitational field equations with a scalar potential $\varphi$ function are derived using the Einstein-Hilbert functional, and the scalar potential $\varphi$ is a natural outcome of the divergence-free constraint of the variational elements.Gravitation is now described by the Riemannian metric$g_{\mu\nu}$, the scalar potential $\varphi$ and their interactions, unified by the new field equations.From quantum field theoretic point of view, the vector field $\Phi_\mu=D_\mu \varphi$, the gradient of the scalar function $\varphi$, is a spin-1 massless bosonic particle field. The field equations induce a natural duality between the graviton (spin-2 massless bosonic particle) and this spin-1 massless bosonic particle. Both particles can be considered as gravitational force carriers, and as they are massless, the induced forces are long-range forces. The (nonlinear) interaction between these bosonic particle fields leads to a unified theory for dark energy and dark matter. Also, associated with the scalar potential $\varphi$ is the scalar potential energy density $\frac{c^4}{8\pi G} \Phi=\frac{c^4}{8\pi G} g^{\mu\nu}D_\mu D_\nu \varphi$, which represents a new type of energy caused by the non-uniform distribution of matter in the universe.The negative part of this potential energy density produces attraction, and the positive part produces repelling force. This potential energy density is conserved with mean zero: $\int_M \Phi dM=0$.The sum of this potential energy density$\frac{c^4}{8\pi G} \Phi$ and the coupling energy between the energy-momentum tensor $T_{\mu\nu}$ and the scalar potential field $\varphi$ gives rise to a unified theory for dark matter and dark energy:The negative part ofthis sum represents the dark matter, which produces attraction,and the positive part represents the dark energy, which drives the acceleration of expanding galaxies.In addition, the scalar curvature of space-time obeys $R=\frac{8\pi G}{c^4} T + \Phi$.Furthermore, the proposed field equations resolve a few difficulties encountered by the classical Einstein field equations.

Vortex counting from field theory

The vortex partition function in 2d $ \mathcal{N} $ = (2, 2) U(N ) gauge theory is derived from the field theoretical point of view by using the moduli matrix approach. The character for the tangent space at each moduli space fixed point is written in terms of the moduli matrix, and then the vortex partition function is obtained by applying the localization formula. We find that dealing with the fermionic zero modes is crucial to obtain the vortex partition function with the anti-fundamental and adjoint matters in addition to the fundamental chiral multiplets. The orbifold vortex partition function is also investigated from the field theoretical point of view.

On a formulation of qubits in quantum field theory

Qubits have been designed in the framework of quantum mechanics. Attempts to formulate the problem in the language of quantum field theory have been proposed already. In this short Letter we refine the meaning of qubits within the framework of quantum field theory. We show that the notion of gauge invariance naturally leads to a generalization of qubits to QFTbits which are then the fundamental carriers of information from the quantum field theoretical point of view. The goal of this Letter is to stress the availability of such a generalized concept of QFTbits.

Beyond Einstein–Cartan gravity: quadratic torsion and curvature invariants with even and odd parity including all boundary terms

Recently, gravitational gauge theories with torsion have been discussed by an increasing number of authors from a classical as well as from a quantum field theoretical point of view. The Einstein–Cartan(–Sciama–Kibble) Lagrangian has been enriched by the parity odd pseudoscalar curvature (Hojman, Mukku and Sayed) and by torsion square and curvature square pieces, likewise of even and odd parity. (i) We show that the inverse of the so-called Barbero–Immirzi parameter multiplying the pseudoscalar curvature, because of the topological Nieh–Yan form, can be appropriately discussed if torsion square pieces are included. (ii) The quadratic gauge Lagrangian with both parities, proposed by Obukhov et al and Baekler et al, emerges also in the framework of Diakonov et al. We establish the exact relations between both approaches by applying the topological Euler and Pontryagin forms in a Riemann–Cartan space expressed for the first time in terms of irreducible pieces of the curvature tensor. (iii) In a Riemann–Cartan spacetime, that is, in a spacetime with torsion, parity-violating terms can be brought into the gravitational Lagrangian in a straightforward and natural way. Accordingly, Riemann–Cartan spacetime is a natural habitat for chiral fermionic matter fields.

Accretion of Chaplygin gas upon black holes: formation of faster outflowing winds

We study the accretion of modified Chaplygin gas upon different types of black holes. Modified Chaplygin gas is one of the best candidates for a combined model of dark matter and dark energy. In addition, from a field theoretical point of view the modified Chaplygin gas model is equivalent to that of a scalar field having a self-interacting potential. We formulate the equations related to both spherical accretion and disc accretion, and respective winds. The corresponding numerical solutions of the flow, particularly of velocity, are presented and analysed. We show that the accretion–wind system of modified Chaplygin gas dramatically alters the wind solutions, producing faster winds, upon changes in physical parameters, while accretion solutions qualitatively remain unaffected. This implies that modified Chaplygin gas is more prone to produce outflow which is the natural consequence of the dark energy into the system.

Quiver gauge theory and extended electric-magnetic duality

We construct N=1 A-D-E quiver gauge theory with the gauge kinetic term which depends on the adjoint chiral superfields, as a low energy effective theory on D5-branes wrapped on 2-cycles of Calabi-Yau 3-fold in IIB string theory. The field-dependent gauge kinetic term can be engineered by introducing B-field which holomorphically varies on the base space (complex plane) of Calabi-Yau. We consider Weyl reflection on A-D-E node, which acts non-trivially on the gauge kinetic term. It is known that Weyl reflection is related to N=1 electric-magnetic duality. Therefore, the non-trivial action implies an extension of the electric-magnetic duality to the case with the field-dependent gauge kinetic term. We show that this extended duality is consistent from the field theoretical point of view. We also consider the duality map of the operators.

The gauge theory of dislocations: a uniformly moving screw dislocation

In this paper, we present the equations of motion of a moving screw dislocation in the framework of the translation gauge theory of dislocations. In the gauge field theoretical formulation, a dislocation is a massive gauge field. We calculate the gauge field theoretical solutions of a uniformly moving screw dislocation. We give the subsonic and supersonic solutions. Thus, supersonic dislocations are not forbidden from the field theoretical point of view. We show that the elastic divergences at the dislocation core are removed. We also discuss the Mach cones produced by supersonic screw dislocations.

Application of Representation Theory to Dual-Mode Microwave Bandpass Filters

This paper discusses the physics behind the operation of dual-mode bandpass filters from a field theoretical point of view. It is argued that the two degenerate modes of the empty dual-mode cavity, commonly taken as the vertical and horizontal polarizations, become nonphysical when coupling and tuning elements are inserted. Instead, the original degenerate modes are rotated, or modified in a complex way, to generate two new modes whose characteristics depend on the coupling and tuning elements. It is shown that the tuning elements, as placed in existing dual-mode filter designs, act as both tuning and coupling elements. A working dual-mode filter can be designed with only ldquotuningrdquo elements present. A physical representation of dual-mode filters in terms of the eigenresonances of the dual-mode cavities, with the tuning and coupling elements present, is introduced. Two fourth-order dual-mode rectangular cavity filters with the same response in the passband and its vicinity are also presented to demonstrate the similar role played by ldquotuningrdquo and coupling elements in dual-mode cavities. The first filter uses only ldquotuningrdquo elements, while the second is based only on ldquocouplingrdquo elements.

Modularity of Calabi-Yau varieties and conformal field theory

We study the modularity problem of Calabi-Yau varieties from the conformal field theoretic point of view. We express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dedekind eta functions, which is hoped to shed light on the modularity questions for higher dimensional Calabi-Yau varieties.