34 research outputs found
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
Energy-momentum tensors with worldline numerics
We apply the worldline formalism and its numerical Monte-Carlo approach to
computations of fluctuation induced energy-momentum tensors. For the case of a
fluctuating Dirichlet scalar, we derive explicit worldline expressions for the
components of the canonical energy-momentum tensor that are straightforwardly
accessible to partly analytical and generally numerical evaluation. We present
several simple proof-of-principle examples, demonstrating that efficient
numerical evaluation is possible at low cost. Our methods can be applied to an
investigation of positive-energy conditions.Comment: 10 pages, 3 figures, Contribution to QFEXT1
Scalar and Spinor Field Actions on Fuzzy : fuzzy as a bundle over
We present a manifestly Spin(5) invariant construction of squashed fuzzy
as a fuzzy bundle over fuzzy . We develop the necessary
projectors and exhibit the squashing in terms of the radii of the and
. Our analysis allows us give both scalar and spinor fuzzy action
functionals whose low lying modes are truncated versions of those of a
commutative .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
Three-loop Euler-Heisenberg Lagrangian in 1+1 QED, part 1: single fermion-loop part
We study the three-loop Euler-Heisenberg Lagrangian in spinor quantum
electrodynamics in 1+1 dimensions. In this first part we calculate the
one-fermion-loop contribution, applying both standard Feynman diagrams and the
worldline formalism which leads to two different representations in terms of
fourfold Schwinger-parameter integrals. Unlike the diagram calculation, the
worldline approach allows one to combine the planar and the non-planar
contributions to the Lagrangian. Our main interest is in the asymptotic
behaviour of the weak-field expansion coefficients of this Lagrangian, for
which a non-perturbative prediction has been obtained in previous work using
worldline instantons and Borel analysis. We develop algorithms for the
calculation of the weak-field expansions coefficients that, in principle, allow
their calculation to arbitrary order. Here for the non-planar contribution we
make essential use of the polynomial invariants of the dihedral group D4 in
Schwinger parameter space to keep the expressions manageable. As expected on
general grounds, the coefficients are of the form r1+r2*zeta(3) with rational
numbers r1, r2. We compute the first two coefficients analytically, and four
more by numerical integration.Comment: 50 pages, 8 figure
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
and 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