Mixed symmetry tensors in the worldline formalism

We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which - by adding a suitable Chern-Simons term to the particle action - can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) "flavour" symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young Tableau. In particular the occupation numbers of the wavefunction - i.e. the lengths of the columns (rows) of the Young Tableau - are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.Comment: 1+32 page

U(N) Yang-Mills in non-commutative space time

We present an approach to U c6 (N) Yang-Mills theory in non-commutative space based upon a novel phase-space analysis of the dynamical fields with additional auxiliary variables that generate Lorentz structure and colour degrees of freedom. To illustrate this formalism we compute the quadratic terms in the effective action focusing on the planar divergences so as to extract the \u3b2-function for the Yang-Mills coupling constant. Nonetheless the method presented is general and can be applied to calculate the effective action at arbitrary order of expansion in the coupling constant and is well suited to the computation of low energy one-loop scattering amplitudes

One-particle reducible contribution to the one-loop spinor propagator in a constant field

Extending work by Gies and Karbstein on the Euler\ue2\u80\u93Heisenberg Lagrangian, it has recently been shown that the one-loop propagator of a charged scalar particle in a constant electromagnetic field has a one-particle reducible contribution in addition to the well-studied irreducible one. Here we further generalize this result to the spinor case, and find the same relation between the reducible term, the tree-level propagator and the one-loop Euler\ue2\u80\u93Heisenberg Lagrangian as in the scalar case. Our demonstration uses a novel worldline path integral representation of the photon-dressed spinor propagator in a constant electromagnetic field background

Mixed symmetry Wilson-loop interactions in the worldline formalism

Using the worldline formalism of the Dirac field with a non-Abelian gauge symmetry we show how to describe the matter field transforming in an arbitrary representation of the gauge group. Colour degrees of freedom are carried on the worldline by auxiliary fields, responsible for providing path ordering and the Wilson-loop coupling. The Hilbert space of these fields is reducible but we make use of recent work in order to project onto a single, arbitrary, irreducible representation. By functionally quantising the resulting theory we show that this procedure correctly generates the Wilson-loop interaction between the gauge field and the matter field taken to transform in a chosen representation. This work has direct application to physical observables such as scattering amplitudes in the presence of such a matter multiplet and lifts the restriction on the type of matter that has previously featured in worldline calculations.Comment: 47 Pages, 2 Appendices. Update to version accepted for publicatio

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

A Remark on Non-conformal Non-supersymmetric Theories with Vanishing Vacuum Energy Density

We discuss non-conformal non-supersymmetric large N gauge theories with vanishing vacuum energy density to all orders in perturbation theory. These gauge theories can be obtained via a field theory limit of Type IIB D3-branes embedded in orbifolded space-times. We also discuss gravity in this setup.Comment: 13 pages, revtex; a minor change in wordin

The Effects of the COVID-19 Pandemic on the Tourism Industry in Negros Oriental, Philippines

The study tries to determine the effects of the pandemic on the tourism industry in Negros Oriental specifically on accommodation facilities and food and beverage establishments. This study is a descriptive method using the correlational technique. The results show that both accommodation facilities and F&B establishments strongly agree that the actions taken during the pandemic are the observance of government protocols. The study also finds out a significant relationship between human resources and operating pressures with actions taken during the pandemic. While for the F&B establishments, human resources, operations, financial situations, operating pressures, and government policies shows a significant relationship to actions taken during the pandemic. It is also said that accommodation facilities that manage by women take action effectively during the pandemic, and accommodations facilities with more employees have more operating pressures compared to businesses with fewer employees. The same can be said with F&B establishments where sex and marital status is significantly related to human resource. This means that F&B establishments managed by single women experienced less effect on their human resources and single women can work effectively during the pandemic

New Relativistic Effects in the Dynamics of Nonlinear Hydrodynamical Waves

In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity. When the fluid is allowed to relax, one of three possible wave-patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a special relativistic Riemann problem when velocities tangential to the initial discontinuity surface are present. We show that a smooth transition from one wave-pattern to another can be produced by varying the initial tangential velocities while otherwise maintaining the initial states unmodified. These special relativistic effects are produced by the coupling through the relativistic Lorentz factors and do not have a Newtonian counterpart.Comment: 4 pages, 5 figure

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.Facultad de Ciencias ExactasInstituto de Física La Plat