Unphysical Sector Research Articles

Nonlinear chiral forms in the Sen formulation

The Sen formulation for chiral (2p)-form in 4p+2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4p+2$$\\end{document} dimensions describes a system with two separate sectors, one is physical while the other is unphysical. Each contains a chiral form and a metric. In this paper, we focus on the cases where the self-duality condition for the unphysical sector is linear while for the physical sector can be nonlinear. We show the decoupling at the Hamiltonian and Lagrangian levels. The decoupling at the Hamiltonian level follows the idea in the literature. Then by an appropriate field redefinition of the corresponding first-order Lagrangian, the separation at the Lagrangian level follows. We derive the diffeomorphism of the theory in the case where the chiral form in the physical sector has nonlinear self-dual field strength and couples to external (2p+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2p+1)$$\\end{document}-form field. Explicit forms of Sen theories are also discussed. The Lagrangian for the quadratic theory is separated into two Henneaux–Teitelboim Lagrangians. We also discuss the method of generating explicit nonlinear theories with p=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=1$$\\end{document}. Finally, we also show that the M5-brane action in the Sen formulation is separated into a Henneaux–Teitelboim action in unphysical sector and a gauge-fixed PST in physical sector.

Low-energy effective field theory below the electroweak scale: one-loop renormalization in the ’t Hooft-Veltman scheme

The low-energy effective field theory below the electroweak scale (LEFT) describes the effects at low energies of both the weak interaction and physics beyond the Standard Model. We study the one-loop renormalization of the LEFT in the ’t Hooft-Veltman scheme, which offers an algebraically consistent definition of the Levi-Civita symbol and γ5 in dimensional regularization. However, in connection with minimal subtraction this scheme leads to a spurious breaking of chiral symmetry in intermediate steps of the calculation. Based on the ’t Hooft-Veltman prescription, we define a renormalization scheme that restores chiral symmetry by including appropriate finite counterterms. To this end, we extend the physical LEFT operator basis by a complete set of off-shell and one-loop-evanescent operators and we perform the renormalization at one loop. We determine the finite counterterms to the physical parameters that compensate both the insertions of evanescent operators, as well as the chiral-symmetry-breaking terms from the renormalizable part of the Lagrangian in D dimensions. Our results can be applied in next-to-leading-log calculations in the ’t Hooft-Veltman scheme: using our renormalization scheme instead of pure minimal subtraction separates the physical sector from the unphysical evanescent sector and leads to results that are manifestly free of spurious chiral-symmetry-breaking terms.

A canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics in first-order formalism

We give a canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics by introducing two sets of new variables which help us transform the Lagrangian into an equivalent first-order formalism. After eliminating the unphysical sector, we calculate the physical degrees of freedom of the higher derivative system and obtain the Dirac brackets in the reduced phase space. Then with the aid of the first-class constraints, we construct the independent gauge generator which is closely connected with the BRST charge and the BRST-invariant Hamiltonian. Finally, by choosing appropriate gauge-fixing fermion, we evaluate the path integral of this higher derivative constrained system in BRST quantization scheme with the generalized Lorenz gauge condition.

Unimodular gauge in perturbative gravity and supergravity

This paper explains the Unimodular gauge fixing of gravity and supergravity in the framework of a perturbative BRST construction. The unphysical sector contains additional BRST-exact quartets to suppress possible ambiguities and impose both the Unimodular gauge fixing condition on the metric and a gauge condition for the reparametrization symmetry of the unimodular part of the metric. The Unimodular gauge choice of the metric must be completed by a γ-Traceless gauge condition for the Rarita–Schwinger field in the case of supergravity. This gives an interesting new class of gauges for gravity and supergravity.

On the Lagrangian description of dissipative systems

We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and conserved quantities, like the Hamiltonian, that generate symmetry transformations and do not correspond to observables. We show that there are simple relations among the equations satisfied by these two types of quantities. In the case of the damped harmonic oscillator, from the quantities obtained by the Noether theorem follows the algebra of Feshbach and Tikochinsky. Furthermore, if we consider the whole dynamics, the degrees of freedom separate into a physical and an unphysical sector. We analyze several cases, with linear and nonlinear dissipative forces; the physical consistency of the solutions is ensured, observing that the unphysical sector has always the trivial solution.

Lepton sector phases and their roles in flavor and generalized CP symmetries

We study the effects of considering nontrivial unphysical lepton sector phases on the group theoretical properties of the flavor and generalized CP symmetry elements in the case where there are three light, distinct Majorana neutrino species. We highlight the similarities and differences between the charged lepton and neutrino sectors and further elucidate the group properties of the flavor and generalized CP symmetry elements. We show how the inclusion of these leptonic phases affects the bottom-up constructions of these symmetry elements and discuss the implications for top-down model building based on discrete symmetry groups.

On the Poincaré and Gauge Symmetry of a Model where Vector and Axial Vector Interaction get Mixed up with Different Weight

A $(1+1)$ dimensional model where vector and axial vector interaction get mixed up with different weight is considered with a generalized masslike term for gauge field. Through Poincar\'e algebra it has been made confirm that only a Lorentz covariant masslike term leads to a physically sensible theory as long as the number of constraints in the phase space is two. With that admissible masslike term, phase space structure of this model with proper identification of physical canonical pair has been determined using Diracs' scheme of quantization of constrained system. The bosonized version of the model remains gauge non-invariant to start with. Therefore, with the inclusion of appropriate Wess-Zumino term it is made gauge symmetric. An alternative quantization has been carried out over this gauge symmetric version to determine the phase space structure in this situation. To establish that the Wess-Zumino fields allocates themselves in the un-physical sector of the theory an attempts has been made to get back the usual theory from the gauge symmetric theory of the extended phase-space without hampering any physical principle. It has been found that the role of gauge fixing is crucial for this transmutation.

Living with spontaneously broken BRST symmetry. I. Physical states and cohomology

We address the issue of BRST symmetry breaking in the GZ model, a local, renormalizable, non-perturbative approach to QCD. Explicit calculation of several examples reveals that BRST symmetry breaking apparently afflicts the unphysical sector of the theory, but may be unbroken where needed, in cases of physical interest. Specifically, the BRST-exact part of the conserved energy-momentum tensor and the BRST-exact term in the Kugo-Ojima confinement condition both have vanishing expectation value. We analyze the origin of the breaking of BRST symmetry in the GZ model, and obtain a useful sufficient condition that determines which operators preserve BRST. Observables of the GZ theory are required to be invariant under a certain group of symmetries that includes not only BRST but also others. The definition of observables is thereby sharpened, and excludes all operators known to us that break BRST invariance. We take as a hypothesis that BRST symmetry is unbroken by this class of observables. If the hypothesis holds, BRST breaking is relegated to the unphysical sector of the GZ theory, and its physical states are obtained by the usual cohomological BRST construction. The fact that the horizon condition and the Kugo-Ojima confinement criterion coincide assures that color is confined in the GZ theory.

A spin-foam vertex amplitude with the correct semiclassical limit

Spin-foam models are hoped to provide a dynamics for loop quantum gravity. These start from the Plebanski formulation of gravity, in which gravity is obtained from a topological field theory, BF theory, through constraints, which, however, select more than one gravitational sector, as well as an unphysical degenerate sector. We show this is why terms beyond the needed Feynman-prescribed one appear in the semiclassical limit of the EPRL spin-foam amplitude. By quantum mechanically isolating a single gravitational sector, we modify this amplitude, yielding a spin-foam amplitude for loop quantum gravity with the correct semiclassical limit.

Cancellation of unphysical gauge and ghost degrees of freedom in back reaction.

We study the U(1) Higgs model in spacetime-dependent background fields (a background metric and a background scalar field). Particle creation can occur because of the time-dependence of these background fields. In gauge theories, there is a unphysical sector and consequently unphysical particles may be produced. However, it is shown that produced unphysical particles have no contribution to backreaction to background fields.

Gauge invariance and mass. II. Non-Abelian case.

A gauge-invariant formulation of massive non-Abelian vector bosons is discussed. It involves nonrenormalizable couplings in an unphysical sector. All the possibilities of decoupling this unphysical sector are discussed. They include the unitary gauge which is nonrenormalizable, due to propagator difficulties, and all the possible (Lagrangian and non-Lagrangian) non-Abelian generalizations of the Stueckelberg formalism which allow a continuous massless limit. None of them corresponds to a true gauge. On the basis of this presentation, there clearly exists no formulation of massive non-Abelian vector bosons renormalizable by power counting. It is however possible to find gauges where all the difficulties with renormalizability are confined in vertices involving always an unphysical field, so that it is plausible that the worst divergences cancel in the physical sector.

On the 1‐Loop Renormalization of the Electroweak Standard Model and its Application to Leptonic Processes

AbstractA renormalization scheme for the electroweak standard model is presented in which the electric charge and the masses of the gauge bosons, Higgs particle and fermions are used as physical parameters. The photon is treated such that quantum electrodynamics is contained as a simple substructure. Field renormalization respecting the gauge symmetry gives finite propagators and vertex functions. The Ward identities between the Green functions of the unphysical sector allow a renormalization that maintains the simple pole structure of the propagators in the t'Hooft‐Feynman gauge. We give a complete list of self energies and all renormalization constants also in the unphysical Higgs and ghost sector. Explicit results are given for the renormalized self energies, vertex functions and boxes that enter the evaluation of 1‐loop radiative corrections to fermionic processes.We calculate the 1‐loop radiative corrections to purely leptonic reactions like μ decay, vμμe scattering and μ pair production in e+e−annihilation. A test of the standard model is performed by comparing these low energy data with the results of the PP collider experiments for the W and Z boson masses.

Antisymmetric Tensor Gauge Field in General Covariant Gauges

Recently, Townsend has shown that there exist similarity and dissimilarity between the mode counting of spin 3/2 field and that of antisymmetric tensor gauge field. 11 Especially, one cannot find a mechanism of introducing extra two modes in contrast to the case of spin 3/2 theory where an additional extra Majorana spinor ghost has been introduced by Nielsen. 21 Nielsen adopted the ordinary form of Faddeev-Popov (FP) ghosts c*(rD)c+N(rD)N. On the other hand, Rata iand Kugo 31 have proposed a new formalism of supergravity by adopting the unconventional form of FP ghost ic*(ro) (rD)c. Since the ghosts c and c* of Hata-Kugo obey the second order differential equations, all their components are independent and give rise to eight modes of FP ghosts. There should then exist eight unphysical modes of spin 3/2 field sector which compensate eight modes of FP ghosts. Such an unphysical sector is constructed by introducing the Lagrangian multiplier spinor field B which plays a role of fixing the gauge. The unphysical modes consist of four longitudinal components of cj; 11 and four components of B, and their number is equal to that of FP ghosts. Fronsdal and Hata41 have further shown that such a type of formalism is necessary to construct the interacting theory of higher spin fields so that the unitarity ,:of the physical S-matrix is assured. The present author 51 has also shown that the axial anomaly for the gravitino in the background curved space is obtained by B field not by ghost fields in Hata-Kugo formalism. It is, therefore, desirable to discuss the mode counting of the quantized antisymmetric tensor gauge field by introducing the Lagrangian multiplier fields. We shall start with the following Lagrangian :