Related papers: Loop Equations in Abelian Gauge Theories
For a pure SU(N) gauge theory on the lattice we test if the expectation values of small Wilson loops become volume independent in the large N limit.
On transformation to the Fourier space $({\bf k}, \omega)$, the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations…
The vacuum dynamics of SU(2) and SU(3) lattice gauge theories is studied by means of a gauge-invariant effective action defined using the lattice Schr\"odinger functional at finite temperature. In the case of the SU(3) gauge theory…
The complete $ q\bar{q}$ semirelativistic interaction is obtained as a gauge-invariant function of the Wilson loop and its functional derivatives. The approach is suitable for analytic evaluations as well as for lattice calculations. Here…
Any metric theory of gravity whose interaction with quantum particles is described by a covariant wave equation is equivalent to a vector theory that satisfies Maxwell-type equations identically. This result does not depend on any…
Since the Maxwell theory of electromagnetic phenomena is a gauge theory, it is quite important to evaluate the zero-point energy of the quantized electromagnetic field by a careful assignment of boundary conditions on the potential and on…
Consistency of $GL(3,R)$ gauge theory of gravity coupled with an external electromagnetic field, is studied. It is shown that possible restrictions on Maxwell field can be avoided through introduction of auxiliary fields.
We give a general expression for the static potential energy of the gravitational interaction of two massive particles, in terms of an invariant vacuum expectation value of the quantized gravitational field. This formula holds for…
We consider a fractal Wilson loop $<F_{P}>$ and present physical arguments why this should be a relevant observable in nature. We show for non-compact SU(2) lattice gauge theory in the next to leading order of strong coupling expansion that…
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…
A new non-Abelian gauge transformation for two-forms is introduced. Construction is based on a fixed map from the spacetime to the loop space which attachs a closed loop to each point of the spacetime. It is argued that this set-up is…
Fundamental forces of Nature are described by field theories, also known as gauge theories, based on a local gauge invariance. The simplest of them is quantum electrodynamics (QED), which is an example of an Abelian gauge theory. Such…
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from…
This brief article sums up results obtained in arXiv:0911.2653, which develops a constrained SU(2) lattice gauge theory in the "dipole" approximation. This is a further step toward the issue of a (inhomogeneous) loop quantum cosmology and…
We analyze quantum Yang-Mills theory on $\mathbb{R}^2$ using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian" free fields whose covariance matrix is…
The free Maxwell field theory is quantized in the Lorentz gauge on a two dimensional manifold $M$ with conformally flat background metric. It is shown that in this gauge the theory is equivalent, at least at the classical level, to a…
We present non-perturbative results for U(1) gauge theory in spaces, which include a non-commutative plane. In contrast to the commutative space, such gauge theories involve a Yang-Mills term, and the Wilson loop is complex on the…
The implementation of gauge theories on a four-dimensional anisotropic lattice with two distinct lattice spacings is discussed, with special attention to the case where two axes are finely and two axes are coarsely discretized. Feynman…
We develop an unified algebraic approach to the description of gauge interactions within the framework of a new concept of quantum mechanics. The next step in generalizing the space-time and the action vector space is made. The gauge field…