Infinite-Dimensional Supermanifolds of Solutions in Lagrangian Field Theories with Fermion Fields

1994 ◽  
pp. 53-60
Author(s):  
Thomas Schmitt
Keyword(s):  
Field Theories ◽  
Infinite Dimensional ◽  
Fermion Fields

scholarly journals Some Aspects of Supersymmetric Field Theories with Minimal Length and Maximal Momentum

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Kourosh Nozari ◽  
F. Moafi ◽  
F. Rezaee Balef
Keyword(s):  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Field Theories ◽  
Majorana Fermion ◽  
Fermion Field ◽  
Free Fermion ◽  
Supersymmetric Field Theories ◽  
Fermion Fields ◽  
Maximal Momentum

We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra[x,p] = iℏ(1−βp+2β2p2), whereβis a deformation parameter. We present a deformed supersymmetric algebra in the presence of minimal length and maximal momentum.

scholarly journals p-BRANES AS COMPOSITE ANTISYMMETRIC TENSOR FIELD THEORIES

1998 ◽  
Vol 13 (08) ◽  
pp. 1263-1292 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Tensor Field ◽  
Target Space ◽  
Field Theories ◽  
Antisymmetric Tensor ◽  
Field Equations ◽  
Light Cone Gauge ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Antisymmetric Tensor Field ◽  
Covariant Action

p′-brane solutions to rank p+1 composite antisymmetric tensor field theories of the kind developed by Guendelman, Nissimov and Pacheva are found when the dimensionality of space–time is D=(p+1)+(p′+1). These field theories possess an infinite-dimensional group of global Noether symmetries, that of volume-preserving diffeomorphisms of the target space of the scalar primitive field constituents. Crucial in the construction of p′ brane solutions are the duality transformations of the fields and the local gauge field theory formulation of extended objects given by Aurilia, Spallucci and Smailagic. Field equations are rotated into Bianchi identities after the duality transformation is performed and the Clebsch potentials associated with the Hamilton–Jacobi formulation of the p′ brane can be identified with the duals of the original scalar primitive constituents. Explicit examples are worked out the analog of S and T duality symmetry are discussed. Different types of Kalb–Ramond actions are given and a particular covariant action is presented which bears a direct relation to the light cone gauge p-brane action.

scholarly journals BRST QUANTIZATION AND THE PRODUCT FORMULA FOR THE RAY-SINGER TORSION

1995 ◽  
Vol 10 (12) ◽  
pp. 1779-1805 ◽  
Author(s):  
CHARLES NASH ◽  
DENJOE O’CONNOR
Keyword(s):  
Finite Elements ◽  
Topological Field Theories ◽  
Brst Quantization ◽  
Product Formula ◽  
Field Theories ◽  
Analytic Torsion ◽  
Quantum Field ◽  
Infinite Dimensional ◽  
New Class ◽  
Topological Field

We give a quantum field theoretic derivation of the formula obeyed by the Ray-Singer torsion on product manifolds. Such a derivation has proved elusive up to now. We use a BRST formalism which introduces the idea of an infinite dimensional Universal Gauge Fermion, and is of independent interest, being applicable to situations other than the ones considered here. We are led to a new class of Fermionic topological field theories. Our methods are also applicable to combinatorially defined manifolds and methods of discrete approximation, such as the use of a simplicial lattice or finite elements. The topological field theories discussed provide a natural link between the combinatorial and analytic torsion.

On the Decomposition of Spinor Fields which satisfy a Nonlinear Higher Order Equation

1983 ◽  
Vol 38 (12) ◽  
pp. 1293-1295
Author(s):  
D. Großer
Keyword(s):  
Field Theory ◽  
Higher Order ◽  
Order Equation ◽  
Field Theories ◽  
First Order ◽  
Spinor Fields ◽  
Fermion Fields ◽  
Higher Derivatives ◽  
Derivatives Of ◽  
Higher Order Equation

Abstract A field theory which is based entirely on fermion fields is non-renormalizable if the kinetic energy contains only derivatives of first order and therefore higher derivatives have to be included. Such field theories may be useful for describing preons and their interaction. In this note we show that a spinor field which satisfies a higher order field equation with an arbitrary nonlinear selfinteraction can be written as a sum of fields which satisfy first order equations.

scholarly journals SINE-GORDON VS. MASSIVE THIRRING

1993 ◽  
Vol 08 (23) ◽  
pp. 4131-4174 ◽  
Author(s):  
TIMOTHY R. KLASSEN ◽  
EZER MELZER
Keyword(s):  
Energy Levels ◽  
Gaussian Model ◽  
Field Theories ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Fermion Fields ◽  
S Matrix

By viewing the sine-Gordon and massive Thirring models as perturbed conformal field theories, one sees that they are different (the difference being observable, for instance, in finite-volume energy levels). The UV limit of the former (SGM) is a Gaussian model, that of the latter (MTM) a so-called fermionic Gaussian model, the compactification radius of the boson underlying both theories depending on the SG/MT coupling. (These two families of conformal field theories are related by a “twist”.) Corresponding SG and MT models contain a subset of fields with identical correlation functions, but each model also has fields the other one does not have; for example, the fermion fields of MTM are not contained in SGM, and the bosonic soliton fields of SGM are not in MTM. Our results imply, in particular, that the SGM at the so-called “free-Dirac point” β2=4π is actually a theory of two interacting bosons with diagonal S-matrix S=−1, and that for arbitrary couplings the overall sign of the accepted SG S-matrix in the soliton sector should be reversed. More generally, we draw attention to the existence of new classes of quantum field theories, analogs of the (perturbed) fermionic Gaussians models, whose partition functions are invariant only under a subgroup of the modular group. One such class comprises “fermionic versions” of the Virasoro minimal models.

scholarly journals INTEGRABLE FIELD THEORIES DERIVED FROM 4-D SELF-DUAL GRAVITY

1996 ◽  
Vol 11 (07) ◽  
pp. 545-552 ◽  
Author(s):  
TATSUYA UENO
Keyword(s):  
Integrable Field Theories ◽  
Sigma Models ◽  
Einstein Equation ◽  
Differential Form ◽  
The Self ◽  
Higgs Bundle ◽  
Field Theories ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Integrable Field

We reformulate the self-dual Einstein equation as a trio of differential form equations for simple two-forms. Using them, we can quickly show the equivalence of the theory and 2-D sigma models valued in infinite-dimensional group, which was shown by Park and Husain earlier. We also derive other field theories including the 2-D Higgs bundle equation. This formulation elucidates the relation among these field theories.

scholarly journals Wilson loops, geometric operators and fermions in 3d group field theory

Open Physics ◽  
2011 ◽  
Vol 9 (4) ◽  
Author(s):  
R. Dowdall
Keyword(s):  
Field Theory ◽  
Wilson Loop ◽  
Vector Fields ◽  
Field Theories ◽  
Tensor Fields ◽  
Spin Network ◽  
Spin Foam Model ◽  
Fermion Fields ◽  
3D Gravity ◽  
Group Field Theory

AbstractGroup field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin network grasping operators which require the introduction of vector fields on the group. We then use this to define group field theories that give a previously defined spin foam model for fermion fields coupled to gravity, and the simpler “quenched” approximation, by using tensor fields on the group. The group field theory naturally includes the sum over fermionic loops at each order of the perturbation theory.

THE HIDDEN KAC-MOODY SYMMETRY OF THE GEOMETRIC ACTIONS

1990 ◽  
Vol 05 (30) ◽  
pp. 2503-2513 ◽  
Author(s):  
H. ARATYN ◽  
E. NISSIMOV ◽  
S. PACHEVA
Keyword(s):  
Group Composition ◽  
General Scheme ◽  
Field Theories ◽  
Coadjoint Orbits ◽  
Arbitrary Field ◽  
Noether Symmetries ◽  
Infinite Dimensional ◽  
Main Application ◽  
Composition Laws ◽  
Geometric Action

A general formalism is proposed to study infinite-dimensional Noether symmetries in arbitrary field theories on group coadjoint orbits as well as in their gauged versions (coset geometric models). The basic tools are generalized group composition laws valid for any geometric action. As a main application, we present a general scheme for constructing the "hidden" Kac-Moody currents.

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