Global existence of coupled Yang-Mills and scalar fields in 2 + 1 dimensional space-time

1981 ◽  
Vol 99 (5) ◽  
pp. 405-410 ◽  
Author(s):  
J. Ginibre ◽  
G. Velo
Keyword(s):  
Global Existence ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Space Time ◽  
Yang Mills ◽  
Dimensional Space Time

scholarly journals About renormalized effective action for the Yang-Mills theory in four-dimensional space-time

2018 ◽  
Vol 191 ◽  
pp. 06001
Author(s):  
A.V. Ivanov
Keyword(s):  
Infinite Series ◽  
Effective Action ◽  
Dimensional Space ◽  
Space Time ◽  
Coupling Constant ◽  
Asymptotic Approach ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Bare Coupling Constant ◽  
Renormalization Theory

This work is related to the asymptotic approach in the renormalization theory and its problems. As the main example, the Yang-Mills theory in four-dimensional space-time is considered. It has been shown earlier [16] that using the asymptotic of the bare coupling constant one can find an expression for the renormalized effective action, however, this formula has problems (divergence ln " and infinite series). This work shows the relation of these values and provides an answer for the renormalized effective action.

QUANTIZATION OF THE LIOUVILLE MODE AND STRING THEORY

1989 ◽  
Vol 04 (11) ◽  
pp. 1033-1041 ◽  
Author(s):  
SUMIT R. DAS ◽  
SATCHIDANANDA NAIK ◽  
SPENTA R. WADIA
Keyword(s):  
String Theory ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Space Time ◽  
Two Dimensions ◽  
General Covariance ◽  
World Sheet ◽  
Lorentzian Signature ◽  
Dimensional Space Time ◽  
Background Fields

We discuss the space-time interpretation of bosonic string theories, which involve d scalar fields coupled to gravity in two dimensions, with a proper quantization of the world-sheet metric. We show that for d>25, the theory cannot describe string modes consistently coupled to each other. For d=25 this is possible; however, in this case the Liouville mode acts as an extra timelike variable and one really has a string moving in 26-dimensional space-time with a Lorentzian signature. By analyzing such a string theory in background fields, we show that the d=25 theory possesses the full 26-dimensional general covariance.

scholarly journals SPIN GAUGE THEORY OF GRAVITY IN CLIFFORD SPACE: A REALIZATION OF KALUZA–KLEIN THEORY IN FOUR-DIMENSIONAL SPACE–TIME

2006 ◽  
Vol 21 (28n29) ◽  
pp. 5905-5956 ◽  
Author(s):  
MATEJ PAVŠIČ
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Dirac Field ◽  
Spin Connection ◽  
Yang Mills ◽  
Object A ◽  
Klein Theory ◽  
Dimensional Space Time ◽  
The Right ◽  
Kaluza Klein

A theory in which four-dimensional space–time is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza–Klein. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U (1) × SU (2) × SU (3) of the standard model. The generalized spin connection in C-space has the properties of Yang–Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb–Ramond fields.

THERMODYNAMIC POTENTIAL FOR SCALAR FIELDS IN SPACE-TIME WITH HYPERBOLIC SPATIAL PART

1992 ◽  
Vol 07 (39) ◽  
pp. 3677-3688 ◽  
Author(s):  
GUIDO COGNOLA ◽  
LUCIANO VANZO
Keyword(s):  
Thermodynamic Potential ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Space Time ◽  
Selberg Trace Formula ◽  
Charged Scalar ◽  
Spatial Part ◽  
Regularization Techniques ◽  
Dimensional Space Time ◽  
Charged Scalar Field

The thermodynamic potential for a charged scalar field of mass m on a (3+1)-dimensional space-time with hyperbolic H3/Γ spatial part is evaluated using zeta-function and heat kernel regularization techniques and Selberg trace formula for co-compact group Γ. High and low temperature expansions are obtained and discussed in detail.

scholarly journals Scenario for the renormalization in the 4D Yang–Mills theory

2016 ◽  
Vol 31 (01) ◽  
pp. 1630001 ◽  
Author(s):  
L. D. Faddeev
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Space ◽  
Background Field ◽  
Space Time ◽  
Quantum Field ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Field Formalism

The renormalizability of the Yang–Mills quantum field theory in four-dimensional space–time is discussed in the background field formalism.

scholarly journals Yang–Mills Theory of Gravity

Physics ◽  
2019 ◽  
Vol 1 (3) ◽  
pp. 339-359
Author(s):  
Malik Al Matwi
Keyword(s):  
Dimensional Space ◽  
Beta Function ◽  
Three Dimensional ◽  
Spin Current ◽  
Space Time ◽  
Yang Mills ◽  
Decomposition Space ◽  
Dimensional Space Time ◽  
Conserved Currents ◽  
Three Dimensional Space

The canonical formulation of general relativity (GR) is based on decomposition space–time manifold M into R × Σ , where R represents the time, and Ksi is the three-dimensional space-like surface. This decomposition has to preserve the invariance of GR, invariance under general coordinates, and local Lorentz transformations. These symmetries are associated with conserved currents that are coupled to gravity. These symmetries are studied on a three dimensional space-like hypersurface Σ embedded in a four-dimensional space–time manifold. This implies continuous symmetries and conserved currents by Noether’s theorem on that surface. We construct a three-form E i ∧ D A i (D represents covariant exterior derivative) in the phase space ( E i a , A a i ) on the surface Σ , and derive an equation of continuity on that surface, and search for canonical relations and a Lagrangian that correspond to the same equation of continuity according to the canonical field theory. We find that Σ i 0 a is a conjugate momentum of A a i and Σ i a b F a b i is its energy density. We show that there is conserved spin current that couples to A i , and show that we have to include the term F μ ν i F μ ν i in GR. Lagrangian, where F i = D A i , and A i is complex S O ( 3 ) connection. The term F μ ν i F μ ν i includes one variable, A i , similar to Yang–Mills gauge theory. Finally we couple the connection A i to a left-handed spinor field ψ , and find the corresponding beta function.

scholarly journals GAUGING YANG–MILLS SYMMETRIES IN (1+1)-DIMENSIONAL SPACE–TIME

2001 ◽  
Vol 16 (29) ◽  
pp. 4713-4768 ◽  
Author(s):  
RAJA Q. ALMUKAHHAL ◽  
TRISTAN HÜBSCH
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Minimal Coupling ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Coupling Type

We present a systematic and "from the ground up" analysis of the "minimal coupling" type of gauging of Yang–Mills symmetries in (2, 2)-supersymmetric (1+1)-dimensional space–time. Unlike in the familiar (3+1)-dimensional N=1 supersymmetric case, we find several distinct types of minimal coupling symmetry gauging, and so several distinct types of gauge (super)fields, some of which entirely novel. Also, we find that certain (quartoid) constrained superfields can couple to no gauge superfield at all, others (haploid ones) can couple only very selectively, while still others (nonminimal, i.e. linear ones) couple universally to all gauge superfields.

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