相关论文: Generalized Quantum Mechanics and Nonlinear Gauge …

The relational formalism based on geometrical clocks and Dirac observables in linearized canonical cosmological perturbation theory is used to introduce an efficient method to find evolution equations for gauge invariant variables. Our…

These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory.…

The current understanding of renormalization in quantum gravity (QG) is based on the fact that UV divergences of effective actions in the covariant QG models are covariant local expressions. This fundamental statement plays a central role…

Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…

This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…

The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and…

Gauge theories on a space-time that is deformed by the Moyal-Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is used to construct gauge invariant…

It is shown that, in order to avoid unacceptable nonlocal effects, the free parameters of the general Doebner-Goldin equation have to be chosen such that this nonlinear Schr\"odinger equation becomes Galilean covariant.

Some non-linear generalizations of classical Radon tomography were recently introduced by M. Asorey et al [Phys. Rev. A 77, 042115 (2008), where the straight lines of the standard Radon map are replaced by quadratic curves (ellipses,…

To describe charged particles interacting with the quantized electromagnetic field, we point out the differences of working in the so-called generalized and the true Coulomb gauges. We find an explicit gauge transformation between them for…

We present a model unifying general relativity and quantum mechanics. The model is based on the (noncommutative) algebra \mbox{{\cal A}} on the groupoid \Gamma = E \times G where E is the total space of the frame bundle over spacetime, and…

We are taught that gauge transformations in classical and quantum mechanics do not change the physics of the problem. Nevertheless here we discuss three broad scenarios where under gauge transformations: (i) conservation laws are not…

We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzezinski and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. We…

The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by…

Gauge-invariant quantum fields are constructed in an Abelian power-counting renormalizable gauge theory with both scalar, vector and fermionic matter content. This extends previous results already obtained for the gauge-invariant…

We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…

First, we point out that the present applied superposition principle is linear, it must be developed into a generality. Next, the linear operators and equations should be developed nonlinearly. They will include nonlinear Klein-Gordon…

Within the framework of the algebraic approach the problem of hidden parameters in quantum mechanics is surveyed. It is shown that the algebraic formulation of quantum mechanics permits introduction of a specific hidden parameter, which has…

The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers…

We propose a generalization of the stochastic gauge fixing procedure for the stochastic quantization of gauge theories where not only the drift term of the stochastic process is changed but also the Wiener process itself. All gauge…