Related papers: Covariant Extended Phase Space for Fields on Curve…
Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of…
How can one fully harness the power of physics encoded in relativistic $N$-body phase space? Topologically, phase space is isomorphic to the product space of a simplex and a hypersphere and can be equipped with explicit coordinates and a…
In this paper, we show how the motion of physical fields, in particular the electromagnetic potential, is connected with the choice of a space and time decomposition of the background spacetime manifold. The relation of the field dynamics…
A geometrical interpretation of Schr\"odinger's kinetic and potential energy operators is proposed, allowing for a covariant momentum space formulation of the dynamics that is relevant for the theories with the deformation of the momentum…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
We use covariant phase space methods to study the metric and tetrad formulations of General Relativity in a manifold with boundary and compare the results obtained in both approaches. Proving their equivalence has been a long-lasting…
Quantum field theory in curved spacetime may be defined either through a manifestly unitary canonical approach or via the manifestly covariant path integral formalism. For gauge theories, these two approaches have produced conflicting…
We explain that when quantising phase spaces with varying symplectic structures, the bundle of quantum Hilbert spaces over the parameter space has a natural unitary connection. We then focus on symplectic vector spaces and their fermionic…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phase-space techniques are known, however a thorough…
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…
We disscuss some geometric aspects of the concept of non-Noether symmetry. It is shown that in regular Hamiltonian systems such a symmetry canonically leads to a Lax pair on the algebra of linear operators on cotangent bundle over the phase…
We present a topological quantization of free massive bosonic fields as the first example of a classical field theory with a quantum counterpart to be studied under this formalism. First, we identify certain harmonic map as a geometric…
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…
With the covariant formulation in hand from the first paper of this series (physics/9801019), we begin in this second paper to study the canonical (or ``instantaneous'') formulation of classical field theories. The canonical formluation…
The formalism for histories-based generalized quantum mechanics developed in two earlier papers is applied to the treatment of histories (of particles or fields or more general objects) in curved spacetimes (which need not admit foliation…
We develop a covariant density matrix approach to kinetic theory of QED plasmas subjected into a strong external electromagnetic field. A canonical quantization of the system on space-like hyperplanes in Minkowski space and a covariant…
Based on the concept of curved spacetime in Einsteinian General Relativity, the field theories and their quantum theories in the curved octonion spaces etc are discussed. The research results discover the close relationships of the curved…
The quantum space-time and the phase space with fuzzy structure is investigated as the possible quantization formalism. In this theory the state of nonrelativistic particle corresponds to the element of fuzzy ordered set (Foset) - fuzzy…