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We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
We introduce a new class of unitary transformations based on the su(1,1) Lie algebra that generalizes, for certain particular representations of its generators, well-known squeezing transformations in quantum optics. To illustrate our…
The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…
The exact solution of the Lindblad equation with a quadratic Hamiltonian and linear coupling operators was derived within the chord representation, that is, for the Fourier transform of the Wigner function, also known as the characteristic…
The classical limit for generalized partition functions is obtained using coherent states. In this framework it is presented a general procedure to obtain all the corrections to the classical limit. In particular, the first and second order…
The Lindblad quantum master equation is one of the central approaches to the physics of open quantum systems. In particular, boundary driving enables the study of transport, where a steady state emerges in the long-time limit, which…
Recently a paper on the construction of consistent Wigner functions for cylindrical phase spaces S^1 x R, i.e. for the canonical pair angle and angular momentum, was presented (arXiv:1601.02520), main properties of those functions derived,…
Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It…
Operators in quantum mechanics - either observables, density or evolution operators, unitary or not - can be represented by c-numbers in operator bases. The position and momentum bases are in one to one correspondence with lagrangian planes…
The statistical model of quantum mechanics is based on the mapping between operators on the Hilbert space and functions on the phase space. This map can be implemented by an operator that satisfies physically motivated Stratonovich-Weyl…
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of…
We propose a modification of a recently introduced generalized translation operator, by including a $q$-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator $\hat{p}_q$, and its canonically…
While the notion of open quantum systems is itself old, most of the existing studies deal with quantum mechanical systems rather than quantum field theories. After a brief review of field theoretical/path integral tools currently available…
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…
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…
The Madelung transformation of the space in which a quantum wave function takes its values is generalized from complex numbers to include field spaces that contain orbits of groups that are diffeomorphic to spheres. The general form for the…
The Wigner-Weyl- Moyal approach to Quantum Mechanics is recalled, and similarities to classical probability theory emphasised. The Wigner distribution function is generalised and viewed as a construction of a bosonic object, a target space…
A theory of nonunitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. Exact solutions of the transformation kernels and the phase space propagators are given for…
Following the discussion -- in state space language -- presented in a preceding paper, we work on the passage from the phase space description of a degree of freedom described by a finite number of states (without classical counterpart) to…