Related papers: Exact Path Integrals by Equivariant Cohomology
Quantum cellular automata have been recently considered as a fundamental approach to quantum field theory, resorting to a precise automaton, linear in the field, for the Dirac equation in one dimension. In such linear case a quantum…
In this talk we briefly review the concept of supersymmetric quantum mechanics using a model introduced by Witten. A quasi-classical path-integral evaluation for this model is performed, leading to a so-called supersymmetric quasi-classical…
Equivariant cohomology, a captivating fusion of symmetry and abstract mathematics, illuminates the profound role of group actions in shaping geometric structures. At its core lies the Atiyah-Bott Localization Theorem, a mathematical jewel…
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex…
Equivalence checking of quantum circuits is a central verification task in quantum computing, ensuring the correctness of circuit optimizations, hardware mappings, and compilation pipelines. Among the primary symbolic methods for this…
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…
We apply the technique of complex paths to obtain Hawking radiation in different coordinate representations of the Schwarzschild space-time. The coordinate representations we consider do not possess a singularity at the horizon unlike the…
We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant…
Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by…
Let Gamma be a congruence subgroup of the Picard modular group of an imaginary number field k, and let D be the associated symmetric space. We describe a method to compute the integral cohomology of the locally symmetric space Gamma\D. The…
The algebraic approach to quantum mechanics has been vital to the development of quantum theory since its inception, and it has evolved into a mathematically rigorous $C^\ast$-algebraic formulation of the theory's axioms. Conversely, the…
This model is one of the possible geometrical interpretations of Quantum Mechanics where found to every image Path correspondence the geodesic trajectory of classical test particles in the random geometry of the stochastic fields…
The hyperplane and proper time formalisms are discussed mainly for the spin-half particles in the quantum case. A connection between these covariant Hamiltonian formalisms is established. It is showed that choosing the space-like…
The shift in chemical equilibria due to isotope substitution is often exploited to gain insight into a wide variety of chemical and physical processes. It is a purely quantum mechanical effect, which can be computed exactly using…