Worldline Numerics for Energy-Momentum Tensors in Casimir Geometries

We develop the worldline formalism for computations of composite operators such as the fluctuation induced energy-momentum tensor. As an example, we use a fluctuating real scalar field subject to Dirichlet boundary conditions. The resulting worldline representation can be evaluated by worldline Monte-Carlo methods in continuous spacetime. We benchmark this worldline numerical algorithm with the aid of analytically accessible single-plate and parallel-plate Casimir configurations, providing a detailed analysis of statistical and systematic errors. The method generalizes straightforwardly to arbitrary Casimir geometries and general background potentials.Comment: 23 pages, 12 figure

Scalar and Spinor Field Actions on Fuzzy S4S^4: fuzzy CP3CP^3 as a SF2S^2_F bundle over SF4S^4_F

We present a manifestly Spin(5) invariant construction of squashed fuzzy $CP^3$ as a fuzzy $S^2$ bundle over fuzzy $S^4$. We develop the necessary projectors and exhibit the squashing in terms of the radii of the $S^2$ and $S^4$. Our analysis allows us give both scalar and spinor fuzzy action functionals whose low lying modes are truncated versions of those of a commutative $S^4$.Comment: 19 page

Group invariants for Feynman diagrams

It is well-known that the symmetry group of a Feynman diagram can give important information on possible strategies for its evaluation, and the mathematical objects that will be involved. Motivated by ongoing work on multi-loop multi-photon amplitudes in quantum electrodynamics, here I will discuss the usefulness of introducing a polynomial basis of invariants of the symmetry group of a diagram in Feynman-Schwinger parameter space.Comment: 9 pages, 8 figures, talk given by C. Schubert at 34th International Colloquium on Group Theoretical Methods in Physics, Strasbourg, 18-22 July 202

Non-perturbative Quantum Propagators in Bounded Spaces

We outline a new approach to calculating the quantum mechanical propagator in the presence of geometrically non-trivial Dirichlet boundary conditions based upon a generalisation of an integral transform of the propagator studied in previous work (the so-called ``hit function''), and a convergent sequence of Pad\'e approximants. In this paper the generalised hit function is defined as a many-point propagator and we describe its relation to the sum over trajectories in the Feynman path integral. We then show how it can be used to calculate the Feynman propagator. We calculate analytically all such hit functions in $D=1$ and $D=3$ dimensions, giving recursion relations between them in the same or different dimensions and apply the results to the simple cases of propagation in the presence of perfectly conducting planar and spherical plates. We use these results to conjecture a general analytical formula for the propagator when Dirichlet boundary conditions are present in a given geometry, also explaining how it can be extended for application for more general, non-localised potentials. Our work has resonance with previous results obtained by Grosche in the study of path integrals in the presence of delta potentials. We indicate the eventual application in a relativistic context to determining Casimir energies using this technique.Comment: 26 pages,6 figures, 5 appendice

Worldline formalism for a confined scalar field

The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first quantization of an auxiliary point-particle whose transition amplitudes correspond to the heat-kernel of the operator of quantum fluctuations of the field theory. However, to study a quantum field which is confined within some boundaries one needs to restrict the path integration domain of the auxiliary point-particle to a specific subset of worldlines enclosed by those boundaries. We show how to implement this restriction for the case of a scalar field confined to the D-dimensional ball under Dirichlet and Neumann boundary conditions, and compute the first few heat-kernel coefficients as a verification of our construction. We argue that this approach could admit different generalizations.Fil: Corradini, Olindo. Università Di Modena E Reggio Emilia.; Italia. Istituto Nazionale Di Fisica Nucleare; ItaliaFil: Edwards, James P.. Universidad Michoacana de San Nicolás de Hidalgo; MéxicoFil: Huet, Idrish. Universidad Nacional Autónoma de México; MéxicoFil: Manzo, Lucas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: González Pisani, Pablo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

Scalar and spinor field actions on fuzzy S4: fuzzy CP3 as a S2F bundle over S4F

We present a manifestly Spin(5) invariant construction of s quashed fuzzy CP3 as a fuzzy S2 bundle over fuzzy S4 . We develop the necessary projectors and exhibit the squashing in terms of the radii of the S2 and S4 . Our analysis allows us give both scalar and spinor fuzzy action functionals whose low lying modes are truncated versions of those of a commutative S4

Scalar and spinor field actions on fuzzy S4: fuzzy CP3 as a S2F bundle over S4F

We present a manifestly Spin(5) invariant construction of s quashed fuzzy CP3 as a fuzzy S2 bundle over fuzzy S4 . We develop the necessary projectors and exhibit the squashing in terms of the radii of the S2 and S4 . Our analysis allows us give both scalar and spinor fuzzy action functionals whose low lying modes are truncated versions of those of a commutative S4