arXiv subjects

Brenden McDearmon

Publications and source records attributed to Brenden McDearmon.

4 recordsLinked to original sources

arXiv2024

A relativistic statistical field theory on a discretized Minkowski lattice with quantum-like observables

A relativistic statistical field theory is constructed for a fluctuating complex-valued scalar field on a discretized Minkowski lattice. A Hilbert space of observables is then constructed from functionals of the fluctuating complex-valued scalar field with an inner product defined in terms of expectation values of the functionals. A bosonic Fock space is then constructed from the Hilbert space and creation and annihilation operators that act on the Fock space are defined. The creation and annihilation operators are used to define field operators. These field operators have some interesting quantum-like properties. For example, the field operators do not commute in general and, in the particular case of the free field theory, can be shown to satisfy the microcausality condition.

quant-ph↗

arXiv2024

A momentum space formulation for some relativistic statistical field theories with quantum-like observables

Considering a fluctuating scalar field on momentum space, some relativistic statistical field theories are constructed. A Hilbert space of observables is then constructed from functionals of the fluctuating scalar field with an inner product defined in terms of expectation values of the functionals. A bosonic Fock space is then constructed from the Hilbert space and creation and annihilation operators that act on the Fock space are defined. The creation and annihilation operators are used to define field operators. These field operators have some interesting quantum-like properties. For example, the field operators do not commute in general and, in the particular case of the free field theory, can be shown to satisfy the microcausality condition.

quant-ph↗

arXiv2023

Euclidean Quantum Gravity from Variational Dynamics

A variational phase space is constructed for a compact and piecewise flat Riemannian manifold. An extended action functional is provided such that the variational dynamics generate a symplectic flow on the phase space. This symplectic flow is numerically integrated as it evolves with respect to the variational parameter. Assuming ergodicity, the resulting flow samples the Euclidean path integral.

gr-qc↗

arXiv2023

Euclidean Quantum Field Theory from Variational Dynamics

A variational phase space is constructed for a system of fields on Euclidean space with periodic boundary conditions. An extended action functional is defined such that the Euler-Lagrange equations generate a symplectic flow on the variational phase space. This symplectic flow is numerically integrated as it evolves with respect to the variational parameter. Assuming ergodicity, the resulting flow samples the Euclidean path integral.

hep-lat↗