scholarly journals Coupling of a vector gauge field to a massive tensor field

2004 ◽  
Vol 596 (3-4) ◽  
pp. 301-305 ◽  
Author(s):  
S.V. Kuzmin ◽  
D.G.C. McKeon
Keyword(s):  
Gauge Field ◽  
Tensor Field ◽  
Vector Gauge

scholarly journals Consistent Interactions in Terms of the Generalized Fields Method

1997 ◽  
Vol 12 (24) ◽  
pp. 4387-4397 ◽  
Author(s):  
Ömer F. Dayi
Keyword(s):  
Master Equation ◽  
Gauge Field ◽  
Tensor Field ◽  
General Scheme ◽  
Antisymmetric Tensor ◽  
Four Dimensions ◽  
Bf Theory ◽  
Free Theory ◽  
Antisymmetric Tensor Field

The interactions which preserve the structure of the gauge interactions of the free theory are introduced in terms of the generalized fields method for solving the Batalin–Vilkovisky master equation. It is shown that by virtue of this method the solution of the descent equations resulting from the cohomological analysis is provided straightforwardly. The general scheme is illustrated by applying it to the spin 1 gauge field in three and four dimensions, to free BF theory in 2D, and to the antisymmetric tensor field in any dimension. It is shown that it reproduces the results obtained by cohomological techniques.

scholarly journals Hamiltonian formalism of topologically massive electrodynamics

2019 ◽  
Vol 34 (10) ◽  
pp. 1950067 ◽  
Author(s):  
Taegyu Kim ◽  
Seyen Kouwn ◽  
Phillial Oh
Keyword(s):  
Gauge Field ◽  
Tensor Field ◽  
Hamiltonian Formalism ◽  
Higgs Mechanism ◽  
Canonical Analysis ◽  
Antisymmetric Tensor ◽  
Antisymmetric Tensor Field ◽  
Topological Interaction

We consider the four-dimensional topologically massive electrodynamics in which a gauge field interacts with rank two antisymmetric tensor field through a topological interaction. The photon becomes massive by eating the rank two tensor field, which is dual to the Higgs mechanism. We explicitly demonstrate the nature of the mechanism by performing a canonical analysis of the theory and discuss various aspects of it.

scholarly journals Partition functions of higher derivative conformal fields on conformally related spaces

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Jyotirmoy Mukherjee
Keyword(s):  
Partition Function ◽  
Integral Representation ◽  
Gauge Field ◽  
Partition Functions ◽  
Conformal Vector ◽  
Higher Derivative ◽  
Conformal Fields ◽  
Vector Gauge ◽  
Bulk Part ◽  
Hyperbolic Cylinders

Abstract The character integral representation of one loop partition functions is useful to establish the relation between partition functions of conformal fields on Weyl equivalent spaces. The Euclidean space Sa × AdSb can be mapped to Sa+b provided Sa and AdSb are of the same radius. As an example, to begin with, we show that the partition function in the character integral representation of conformally coupled free scalars and fermions are identical on Sa × AdSb and Sa+b. We then demonstrate that the partition function of higher derivative conformal scalars and fermions are also the same on hyperbolic cylinders and branched spheres. The partition function of the four-derivative conformal vector gauge field on the branched sphere in d = 6 dimension can be expressed as an integral over ‘naive’ bulk and ‘naive’ edge characters. However, the partition function of the conformal vector gauge field on $$ {S}_q^1 $$ S q 1 × AdS5 contains only the ‘naive’ bulk part of the partition function. This follows the same pattern which was observed for the partition of conformal p-form fields on hyperbolic cylinders. We use the partition function of higher derivative conformal fields on hyperbolic cylinders to obtain a linear relationship between the Hofman-Maldacena variables which enables us to show that these theories are non-unitary.

Nonplanar graphs and anomalies in chiral noncommutative gaugetheories

2005 ◽  
Vol 83 (10) ◽  
pp. 1051-1061 ◽  
Author(s):  
Marie Gagne-Portelance ◽  
D.G.C. McKeon
Keyword(s):  
Gauge Field ◽  
Fermion Field ◽  
Gauge Model ◽  
Surface Term ◽  
Loop Momentum ◽  
Axial Gauge ◽  
Momentum Variable ◽  
Vector Gauge ◽  
Nonplanar Surface

The AV (n) one-loop graphs are examined in a 2n-dimensional massless noncommutative gauge model in which both a U(1) axial gauge field A and a U(1) vector gauge field V have adjoint couplings to a Fermion field. A possible anomaly in the divergence of the n + 1 vertices is examined by considering the surface term that can possibly arise when shifting the loop momentum variable of integration. It is shown that despite the fact that the graphs are nonplanar, surface terms do arise in individual graphs, but that in 4n dimensions, a cancellation between the surface term contribution coming from pairs of graphs eliminates all anomalies, while in 4n + 2 dimensions such a cancellation cannot occur and an anomaly necessarily arises.PACS No.: 11.30.Rd

A THREE-DIMENSIONAL GAUGE THEORY COUPLED TO FERMIONIC SCALARS AND VECTORS

1994 ◽  
Vol 09 (30) ◽  
pp. 5359-5367 ◽  
Author(s):  
D.G.C. McKEON
Keyword(s):  
Gauge Theory ◽  
Vector Field ◽  
Temperature Dependence ◽  
Gauge Field ◽  
Gauge Transformation ◽  
Lorentz Transformation ◽  
Spinor Field ◽  
Tensor Field ◽  
Three Dimensional ◽  
Radiative Corrections

By involving the group indices of an SU(2) gauge theory in three Euclidean dimensions in the Lorentz transformation, one finds that the gauge field can be decomposed into a scalar, vector and tensor field which mix under a gauge transformation. It is shown how this gauge field can be coupled to an O(3) spinor field whose transformation properties allow one to decompose it into a fermionic scalar and a fermionic vector field. Radiative corrections must be done in a way that respects the dimensionality of the theory; it is demonstrated how operator regularization can be used to this end by computing the temperature dependence of the η function arising from spinors.

COMPOSITE CHERN-SIMONS GAUGE BOSON IN ANYON GAS

1991 ◽  
Vol 05 (01n02) ◽  
pp. 391-401
Author(s):  
NGUYEN VAN HIEU ◽  
NGUYEN HUNG SON
Keyword(s):  
Gauge Field ◽  
Gauge Boson ◽  
Effective Action ◽  
Momentum Dependence ◽  
Composite Boson ◽  
Dispersion Equations ◽  
Vector Gauge ◽  
Chern Simons

It was shown that in a free anyon gas there exists a composite vector gauge field with the effective action containing a Chern-Simons term. The momentum dependence of the energy of the composite boson was found. The mixing between Chern-Simons boson and photon gives rise to the appearance of new quasiparticles -Chern-Simons polaritons. The dispersion equations of Chern-Simons polaritons were derived.

On using the Freedman–Townsend model to generate massive vectors

1991 ◽  
Vol 69 (10) ◽  
pp. 1249-1255 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Gauge Field ◽  
Degrees Of Freedom ◽  
Longitudinal Mode ◽  
Energy Scale ◽  
Tree Level ◽  
Gauge Invariant ◽  
Longitudinal Modes ◽  
Vector Gauge ◽  
Dynamical Degrees ◽  
Scalar Mode

The Freedman–Townsend model involves a gauge invariant coupling of an antisymmetric tensor field [Formula: see text] to a non-Abelian vector gauge field [Formula: see text] and an auxiliary gauge field [Formula: see text]. We analyze the dynamical degrees of freedom in this model and investigate unitarity by considering several four-point functions at the tree level. The model is found to describe a massive vector meson with the transverse degrees of freedom residing in [Formula: see text] and the longitudinal degree of freedom in [Formula: see text]. If an extra gauge-invariant term involving the square of the divergence of [Formula: see text] is added to the Lagrangian, then a scalar polarization appears in this field and [Formula: see text] is no longer simply auxiliary. This scalar mode serves to cancel the bad ultraviolet behaviour of the longitudinal mode, but only at the expense of having no lower bound to the energy spectrum of the theory. Furthermore, an examination of four-point tree level graphs indicates that if we consider elastic scattering of longitudinal modes, the amplitudes grows with the energy scale of the process, whether or not the scalar mode is present.

Riemann–Weyl in Deleuze's Bergsonism and the Constitution of the Contemporary Physico-Mathematical Space

2015 ◽  
Vol 9 (1) ◽  
pp. 59-87 ◽  
Author(s):  
Martin Calamari
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Fibre Bundle ◽  
History Of Mathematics ◽  
Gauge Field Theory ◽  
Contemporary Science ◽  
Explicit Mention ◽  
History Of ◽  
Key Features ◽  
Bernhard Riemann

In recent years, the ideas of the mathematician Bernhard Riemann (1826–66) have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second chapter of Bergsonism (1966). In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities (manifolds) is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl (1885–1955). This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities (rhizomatic multiplicities, smooth spaces) and profound confrontation with contemporary science (fibre bundle topology and gauge field theory). This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions.

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