Boundary Conditions that Remove Certain Ultraviolet Divergences

In quantum field theory, Hamiltonians contain particle creation and annihilation terms that are usually ultraviolet (UV) divergent. It is well known that these divergences can sometimes be removed by adding counter-terms and by taking limits in which a UV cutoff tends toward infinity. Here, I review a novel way of removing UV divergences: by imposing a type of boundary condition on the wave function. These conditions, called interior-boundary conditions (IBCs), relate the values of the wave function at two configurations linked by the creation or annihilation of a particle. They allow for a direct definition of the Hamiltonian without renormalization or limiting procedures. In the last section, I review another boundary condition that serves to determine the probability distribution of detection times and places on a time-like 3-surface.

Structural Changes of Circularly Defected Monolayer Circular Graphene Nanosheets Upon Mechanical Vibrations

As the strongest and toughest material known, graphene has found numerous applications in various types of sensors. Due to the great influences of the graphene sheet’s geometry on resonance frequency, circular defects could effect on expected results of sensors. Circular holes in circular graphene sheets (CGSs) have been modeled with molecular dynamics (MD) simulation in the present work. Then the vibration behavior of intact circular plate and circular sheet with the circular defect has been investigated using frequency-domain analysis (FDD). Furthermore, for validating the used method, the obtained natural frequencies for different graphene sheets have been compared with acquired data in former research. The result of validation showed the accuracy of the used method in this study. The results indicated that by increasing the hole size, the natural frequency of a defected sheet with free edges will be diminished, and with simply-supported interior boundary conditions typically went up. Also, by increasing the hole’s eccentricity, the natural frequency of the defected graphene sheet will be diminished when the hole boundary was subjected to simply-support or free condition.

Multi-time formulation of particle creation and annihilation via interior-boundary conditions

Interior-boundary conditions (IBCs) have been suggested as a possibility to circumvent the problem of ultraviolet divergences in quantum field theories. In the IBC approach, particle creation and annihilation is described with the help of linear conditions that relate the wave functions of two sectors of Fock space: [Formula: see text] at an interior point [Formula: see text] and [Formula: see text] at a boundary point [Formula: see text], typically a collision configuration. Here, we extend IBCs to the relativistic case. To do this, we make use of Dirac’s concept of multi-time wave functions, i.e. wave functions [Formula: see text] depending on [Formula: see text] space-time coordinates [Formula: see text] for [Formula: see text] particles. This provides the manifestly covariant particle-position representation that is required in the IBC approach. In order to obtain rigorous results, we construct a model for Dirac particles in 1+1 dimensions that can create or annihilate each other when they meet. Our main results are an existence and uniqueness theorem for that model, and the identification of a class of IBCs ensuring local probability conservation on all Cauchy surfaces. Furthermore, we explain how these IBCs relate to the usual formulation with creation and annihilation operators. The Lorentz invariance is discussed and it is found that, apart from a constant matrix (which is required to transform in a certain way), the model is manifestly Lorentz invariant. This makes it clear that the IBC approach can be made compatible with relativity.