scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

ZERO ENERGY GAUGE FIELDS AND THE PHASES OF A GAUGE THEORY

1990 ◽  
Vol 05 (14) ◽  
pp. 2783-2798 ◽  
Author(s):  
E.I. GUENDELMAN
Keyword(s):  
Gauge Theory ◽  
Gauge Fields ◽  
Zero Energy ◽  
Massless Particles ◽  
New Approach ◽  
Gauge Transformations ◽  
Definition Of ◽  
Higgs Fields ◽  
Invariant Gauge

A new approach to the definition of the phases of a Poincare invariant gauge theory is developed. It is based on the role of gauge transformations that change the asymptotic value of the gauge fields from zero to a constant. In the context of theories without Higgs fields, this symmetry can be spontaneously broken when the gauge fields are massless particles, explicitly broken when the gauge fields develop a mass. Finally, the vacuum can be invariant under this transformation, this last case can be achieved when the theory has a violent infrared behavior, which in some theories can be connected to a confinement mechanism.

scholarly journals NON-ABELIAN TENSOR GAUGE FIELDS I

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4931-4957 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Large Integer ◽  
Gauge Fields ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Higher Derivatives ◽  
Vector Gauge ◽  
Dimensionless Coupling ◽  
Dimensionless Coupling Constant ◽  
Derivatives Of

We suggest an infinite-dimensional extension of gauge transformations which includes non-Abelian tensor gauge fields. In this extension of the Yang–Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrarily large integer spins. The invariant Lagrangian does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with dimensionless coupling constant.

Uq(2) YANG–MILLS THEORY

1998 ◽  
Vol 13 (04) ◽  
pp. 553-568 ◽  
Author(s):  
H. B. BENAOUM ◽  
M. LAGRAA
Keyword(s):  
Quantum Group ◽  
Gauge Fields ◽  
Yang Mills ◽  
Adequate Definition ◽  
Weinberg Angle ◽  
Definition Of

A Yang–Mills theory is presented using the Uq(2) quantum group. Unlike previous works, no assumptions are required — between the quantum gauge parameters and the quantum gauge fields (or curvature) — to get the quantum gauge variations of the different fields. Furthermore, an adequate definition of the quantum trace is presented. Such a definition leads to a quantum metric, which therefore allows us to construct a Uq(2) quantum Yang–Mills Lagrangian. The Weinberg angle θ is found in terms of this q metric to be [Formula: see text].

scholarly journals CHAPLINE–MANTON INTERACTION VERTICES AND HAMILTONIAN BRST COHOMOLOGY

2000 ◽  
Vol 15 (06) ◽  
pp. 893-903 ◽  
Author(s):  
C. BIZDADEA ◽  
L. SALIU ◽  
S. O. SALIU
Keyword(s):  
Gauge Fields ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Brst Charge ◽  
Brst Cohomology ◽  
Interaction Term ◽  
Chern Simons

Consistent interactions between Yang–Mills gauge fields and an Abelian two-form are investigated by using a Hamiltonian cohomological procedure. It is shown that the deformation of the BRST charge and the BRST-invariant Hamiltonian of the uncoupled model generates the Yang–Mills Chern–Simons interaction term. The resulting interactions deform both the gauge transformations and their algebra, but not the reducibility relations.

scholarly journals UNIFICATION OF SPINS AND CHARGES IN GRASSMANN SPACE?

1995 ◽  
Vol 10 (07) ◽  
pp. 587-595 ◽  
Author(s):  
NORMA MANKOČ-BORŠTNIK
Keyword(s):  
Dimensional Subspace ◽  
Gauge Fields ◽  
Lorentz Transformations ◽  
Tensor Fields ◽  
Grassmann Space ◽  
Yang Mills

In a space of d(d > 5) ordinary and d Grassmann coordinates, fields manifest in an ordinary four-dimensional subspace as spinor (1/2, 3/2), scalar, vector or tensor fields with the corresponding charges, according to two kinds of generators of the Lorentz transformations in the Grassmann space. Vielbeins and spin connections define gauge fields-gravitational and Yang–Mills. For d = 15 the theory offers the unification of all known charges — spins and Yang–Mills charges — of fermionic and bosonic fields and all known interactions.

scholarly journals General Yang–Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical frameworkorFrom Bianchi identities to twisted Courant algebroids

2014 ◽  
Vol 12 (01) ◽  
pp. 1550009 ◽  
Author(s):  
Melchior Grützmann ◽  
Thomas Strobl
Keyword(s):  
Gauge Theories ◽  
Differential Forms ◽  
Coupled System ◽  
Scalar Fields ◽  
Gauge Fields ◽  
Courant Algebroids ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Derived Bracket ◽  
Form Degree

Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such theories can be concisely recombined into what is called a Q-structure or, equivalently, an L∞-algebroid. This has many technical and conceptual advantages: complicated higher bundles become just bundles in the category of Q-manifolds in this approach (the many structural identities being encoded in the one operator Q squaring to zero), gauge transformations are generated by internal vertical automorphisms in these bundles and even for a relatively intricate field content the gauge algebra can be determined in some lines and is given by what is called the derived bracket construction. This paper aims equally at mathematicians and theoretical physicists; each more physical section is followed by a purely mathematical one. While the considerations are valid for arbitrary highest form degree p, we pay particular attention to p = 2, i.e. 1- and 2-form gauge fields coupled nonlinearly to scalar fields (0-form fields). The structural identities of the coupled system correspond to a Lie 2-algebroid in this case and we provide different axiomatic descriptions of those, inspired by the application, including e.g. one as a particular kind of a vector-bundle twisted Courant algebroid.

QUANTUM FIELD THEORY TOOLS: A MECHANISM OF MASS GENERATION OF GAUGE FIELDS

2006 ◽  
Vol 21 (06) ◽  
pp. 1307-1324
Author(s):  
F. V. FLORES-BAEZ ◽  
J. J. GODINA-NAVA ◽  
G. ORDAZ-HERNANDEZ
Keyword(s):  
Gauge Symmetry ◽  
Mass Term ◽  
Higgs Bosons ◽  
Gauge Fields ◽  
Quantum Model ◽  
Mass Generation ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Local Gauge ◽  
Local Gauge Symmetry

We present a simple mechanism for mass generation of gauge fields for the Yang–Mills theory, where two gauge SU (N)-connections are introduced to incorporate the mass term. Variations of these two sets of gauge fields compensate each other under local gauge transformations with the local gauge transformations of the matter fields, preserving gauge invariance. In this way the mass term of gauge fields is introduced without violating the local gauge symmetry of the Lagrangian. Because the Lagrangian has strict local gauge symmetry, the model is a renormalizable quantum model. This model, in the appropriate limit, comes from a class of universal Lagrangians which define a new massive Yang–Mills theories without Higgs bosons.

scholarly journals LOCAL GAUGE FIELDS BASED ON A YANG–MILLS THEORY IN LOOP SPACE

1995 ◽  
Vol 10 (07) ◽  
pp. 1019-1043 ◽  
Author(s):  
SHINICHI DEGUCHI ◽  
TADAHITO NAKAJIMA
Keyword(s):  
Minkowski Space ◽  
Loop Space ◽  
Symmetric Tensor ◽  
Gauge Fields ◽  
Tensor Fields ◽  
Yang Mills ◽  
Rank Tensor ◽  
Stueckelberg Formalism ◽  
Mills Field ◽  
Reparametrization Invariance

We construct a Yang–Mills theory in loop space (the space of all loops in Minkowski space) with the Kac–Moody gauge group in such a way that the theory possesses reparametrization invariance. On the basis of the Yang–Mills theory, we derive the usual Yang–Mills theory and a non-Abelian Stueckelberg formalism extended to local antisymmetric and symmetric tensor fields of the second rank. The local Yang–Mills field and the second-rank tensor fields are regarded as components of a Yang–Mills field on the loop space.

scholarly journals Octonionic ternary gauge field theories revisited

2014 ◽  
Vol 11 (03) ◽  
pp. 1450013 ◽  
Author(s):  
Carlos Castro
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Gauge Field Theory ◽  
Gauge Fields ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Closure Relations ◽  
Nonassociative Geometry

An octonionic ternary gauge field theory is explicitly constructed based on a ternary-bracket defined earlier by Yamazaki. The ternary infinitesimal gauge transformations do obey the key closure relations [δ1, δ2] = δ3. An invariant action for the octonionic-valued gauge fields is displayed after solving the previous problems in formulating a nonassociative octonionic ternary gauge field theory. These octonionic ternary gauge field theories constructed here deserve further investigation. In particular, to study their relation to Yang–Mills theories based on the G2 group which is the automorphism group of the octonions and their relevance to noncommutative and nonassociative geometry.

QUANTUM GAUGE THEORIES

1996 ◽  
Vol 11 (04) ◽  
pp. 699-713 ◽  
Author(s):  
M. LAGRAA
Keyword(s):  
Gauge Theory ◽  
Hopf Algebra ◽  
Algebra Structure ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Hopf Algebra Structure ◽  
Quantum Gauge Theory ◽  
Adequate Definition ◽  
Definition Of ◽  
Invariant Quantum

We consider a gauge theory by taking real quantum groups of nondegenerate bilinear form as a symmetry. The construction of this quantum gauge theory is developed in order to fit with the Hopf algebra structure. In this framework, we show that an appropriate definition of the infinitesimal gauge variations and the axioms of the Hopf algebra structure of the symmetry group lead to the closure of the infinitesimal gauge transformations without any assumption on the commutation rules of the gauge parameters, the connection and the curvature. An adequate definition of the quantum trace is given leading to the quantum Killing form. This is used to construct an invariant quantum Yang–Mills Lagrangian.

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