Related papers: Gauge Fields and Unparticles
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe…
A simplified mathematical approach is presented and used to find a suitable free-field Lagrangian to complete previous work on constructing a gauge theory of CPT transformations. The new Lagrangian is a slight but important modification of…
We propose a dynamical mechanism to induce gauge fields in four dimensional space-time from a single scalar field or a spinor field in higher dimensions. The Born-Oppenheimer treatment of the extra dimensions is an essential ingredient in…
The Lagrangian of self-dual gauge theory in various formulations are reviewed. From these results we see a simple rule and use it to present some new non-covariant Lagrangian based on the decomposition of spacetime into $D=D_1+D_2+D_3$. Our…
These lectures present an elementary introduction to quantum gauge fields. The first aim is to show how, in the tree approximation, gauge invariance follows from covariance and unitarity. This leads to the standard construction of the…
Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier…
The multilevel field-antifield formalism is constructed in a geometrically covariant way without imposing the unimodularity conditions on the hypergauge functions. Thus the previously given version [1,2] is extended to cover the most…
The development of nonabelian gauge fields for last 60 years is reviewed. The new method of quantization of gauge fields applicable beyond perturbation theory is proposed.
Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems,…
A discrete field formalism exposes the physical meaning and origins of gauge fields, their symmetries and singularities. They represent a lack of a stricter field-source coherence.
In this review paper we give a geometrical formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss…
The theory of gauge fields in Theoretical Physics poses several mathematical problems of interest in Differential Geometry and in Field Theory. Below we tackle one of these problems: The existence of a finite system of generators of…
The derivation of Feynman rules for unparticles carrying standard model quantum numbers is discussed. In particular, this note demonstrates that an application of Mandelstam's approach to constructing a gauge-invariant action reproduces for…
Using a gauge covariant operator technique we deduce the path integral for a charged particle in a stationary magnetic field, verifying the "midpoint rule" for the discrete form of the interaction term with the vector potential.
Building on an older method used to derive non-decoupling effects of a heavy Higgs boson in the Standard Model, we describe a general procedure to integrate out heavy fields in the path integral. The derivation of the corresponding…
We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals…
Using Grassmann variant of classical mechanics, we construct Lagrangian dynamics of classical spinning particle in (possibly non-abelian) gauge fields. Quantization of this model is briefly discussed.
Systems with singular higher order- Lagrangians are investigated by using the extended form of the canonical method. Besides, the canonical path integral formulation is generalized using the Hamilton- jacobi formulation to investigate…
The standard procedure for making a global phase symmetry local involves the introduction of a rank 1, vector field in the definition of the covariant derivative. Here it is shown that it is possible to gauge a phase symmetry using fields…
Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize…