Related papers: Phase Space Formulation of S-matrix
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be…
Quantum mechanical phase factors can be related to dynamical effects or to the geometrical properties of a trajectory in a given space - either parameter space or Hilbert space. Here, we experimentally investigate a quantum mechanical phase…
The Hamiltonian of relativistic particles with electric and magnetic dipole moments that interact with an electromagnetic field is determined in the Foldy-Wouthuysen representation. Transition to the semiclassical approximation is carried…
The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the $2\rightarrow 2$ scattering matrix $S_{2\rightarrow 2}$ such space is an infinite dimensional convex space…
Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is…
Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
The S-matrix in the static limit of a dispersion relation has a finite order N and is a matrix of meromorfic functions of energy in the complex plane with cuts. In the elastic case it reduces to N functions connected by the crossing…
Quantum statistical mechanics is formulated as an integral over classical phase space. Some details of the commutation function for averages are discussed, as is the factorization of the symmetrization function used for the grand potential…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition $H^\dagger=H$ on the Hamiltonian, where $\dagger$ represents the mathematical operation of complex conjugation and matrix…
We prove that, for any theory defined over a space-time with boundary, the symplectic form derived in the covariant phase space is equivalent to the one derived from the canonical formalism.
The phase-space of a simple synchronization model is thoroughly investigated. The model considers two-mode stochastic oscillators, coupled through a pulse-like interaction controlled by simple optimization rules. A complex phase space is…
We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems.…
We present the quantum and classical mechanics formalisms for a particle with position-dependent mass in the context of a deformed algebraic structure (named $\kappa$-algebra), motivated by the Kappa-statistics. From this structure we…
We present a general framework connecting global symmetries to the relativistic $S$-matrix through the lens of quantum information theory. Analyzing the 2-to-2 scattering of particles of any helicity, we systematically characterize…
We study integrals of motion and factorizable S-matrices in two-dimensional integrable field theory with boundary. We propose the ``boundary cross-unitarity equation'' which is the boundary analog of the cross-symmetry condition of the…