Related papers: Canonical Gauges in the Path Integral for Parametr…
We discuss the canonical quantization of systems formulated on discrete space-times. We start by analyzing the quantization of simple mechanical systems with discrete time. The quantization becomes challenging when the systems have…
We show that the Classical Constraint Algebra of a Parametrized Relativistic Gauge System induces a natural structure of Conformal Foliation on a Transversal Gauge. Using the theory of Conformal Foliations, we provide a natural Factor…
Here we prove that the classical (respectively, quantum) system, consisting of a particle moving in a static electromagnetic field, is canonically (respectively, unitarily) equivalent to a harmonic oscillator perturbed by a spatially…
The parameter-shift rule is an approach to measuring gradients of quantum circuits with respect to their parameters, which does not require ancilla qubits or controlled operations. Here, I discuss applying this approach to a wider range of…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
Although the path-integral formalism is known to be equivalent to conventional quantum mechanics, it is not generally obvious how to implement path-based calculations for multi-qubit entangled states. Whether one takes the formal view of…
The Classical Coordinate System is geometrical by nature with time being an external variable. Constructing a classical coordinate system employs a point-like signal with infinite speed. In Special Relativity Theory the speed is limited but…
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates.…
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…
The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be…
Among various approaches in proving gauge independence, models containing an explicit gauge dependence are convenient. The well-known example is the gauge parameter in the covariant gauge fixing which is of course most suitable for the…
The measure of distinguishability between two neighboring preparations of a physical system by a measurement apparatus naturally defines the line element of the preparation space of the system. We point out that quantum mechanics can be…
Gauge theories with general covariance are particularly reluctant to quantization. We discuss the example of the Hamiltonian formulation of the relativistic point particle that, despite its apparent simplicity, is of crucial importance…
We present a general formalism for the Hamiltonian description of perturbation theory around any spatially homogeneous spacetime. We employ and refine the Dirac method for constrained systems, which is very well-suited to cosmological…
It is often said that in relativistic quantum physics, a fundamental particle ontology is not viable. However, previous works have shown that certain relativistic quantum field theories can be reformulated as path integrals over particle…
Dealing with a generic time-local non-Markovian master equation, we define current and power to be process-dependent as in classical thermodynamics. Each process is characterized by a symmetry transformation, a gauge of the master equation,…
We observe that the radial gauge can be consistently imposed \emph{together} with the Lorenz gauge in Maxwell theory, and with the harmonic traceless gauge in linearized general relativity. This simple observation has relevance for some…
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…
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…