Related papers: Point Splitting and U(1) Gauge Invariance
In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is quantum electrodynamics -- the theory of electrons interacting with the electromagnetic field -- based on U(1) gauge symmetry.…
It is shown that space-time dependent gauge couplings do not completely break gauge invariance. We demonstrate this in various gauge theories.
Dualities and duality transformations form a well established methodology in various aspects of quantum many body physics and quantum field theories, allowing one to exploit equivalence between models which may naively seem completely…
In this paper, I consider a recent controversy about whether first-class constraints generate gauge transformations in the case of electromagnetism. I argue that there is a notion of gauge transformation, the extended notion, which is…
A conjecture in quantum mechanics states that any quantum canonical transformation can decompose into a sequence of three basic canonical transformations; gauge, point and interchange of coordinates and momenta. It is shown that if one…
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be…
The time-dependent, geometric method for high-energy limits and inverse scattering is applied to nonrelativistic quantum particles in external electromagnetic fields. Both the Schr"odinger- and the Pauli equations in R^2 and R^3 are…
Universal quantum simulations of gauge field theories are exposed to the risk of gauge symmetry violations when it is not known how to compile the desired operations exactly using the available gate set. In this article, we show how time…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with…
A gauge system is a classical field theory where among the fields there are connections in a principal G-bundle over the space-time manifold and the classical action is either invariant or transforms appropriately with respect to the action…
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the…
A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. While the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory…
We present the results of a study of the gauge dependence of spacetime perturbations. In particular, we consider gauge invariance in general, we give a generating formula for gauge transformations to an arbitrary order n, and explicit…
Grid-based discretizations of the time dependent Schr\"odinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice…
It is generally assumed that quantum field theory (QFT) is gauge invariant. However it is well known that non-gauge invariant terms appear in various calculations. This problem was examined in Refs. [3] and [4] and it was shown that at the…
Employing an arbitrary velocity gauge transformation this contribution argues that the breaking of time symmetry is a natural consequence of irreversibility.
The Lagrangians and Hamiltonians of classical field theory require to comprise gauge fields in order to be form-invariant under local gauge transformations. These gauge fields have turned out to correctly describe pertaining elementary…
We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thereby, quantum mechanical systems are seen as dissipatively embedded part of a nonlinear classical structure producing…
A field theory with local transformations belonging to the quantum group SU_q(n) is defined on a classical spacetime, with gauge potentials belonging to a quantum Lie algebra. Gauge transformations are defined for the potentials which lead…