Related papers: Interpolating Between Topologies: Casimir Energies
The ground state energy of a boundary quantum field theory is derived in planar geometry in D+1 dimensional spacetime. It provides a universal expression for the Casimir energy which exhibits its dependence on the boundary conditions via…
Time-symmetric cosmological theories, in which the initial and final states are arranged to have similar features or are independently fixed, have been quite extensively discussed in the literature. However, a more general and perhaps more…
We obtain new expressions for the Casimir energy between plates that are mimicked by the most general possible boundary conditions allowed by the principles of quantum field theory. This result enables to provide the quantum vacuum energy…
Notions of topological free entropy and of free capacity are introduced in the $C^*$-algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.
The consistency of quantum field theories defined on domains with external borders imposes very restrictive constraints on the type of boundary conditions that the fields can satisfy. We analyse the global geometrical and topological…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
The basic thermodynamic quantities for a non-interacting scalar field in a periodic potential composed of either a one-dimensional chain of Dirac $\delta$-$\delta^\prime$ functions or a specific potential with extended compact support are…
We study the Casimir problem as the limit of a conventional quantum field theory coupled to a smooth background. The Casimir energy diverges in the limit that the background forces the field to vanish on a surface. We show that this…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
A thought experiment is formulated to unify quantum mechanics and general relativity in a topological manner. An analysis of the interactions in Nature is then presented. The universal ground state of the constructed theory derives from the…
Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of…
In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero point energies of quantum fields are "real''. On the contrary, Casimir effects can be formulated and Casimir forces can be…
The free energy due to the vacuum fluctuations of matter fields on a classical gravitational background is discussed. It is shown explicitly how this energy is calculated for a non-minimally coupled scalar field in an arbitrary…
I review recent results on conformal field theories in four dimensions and quantum field theories interpolating between conformal fixed points, supersymmetric and non-supersymmetric. The talk is structured in three parts: i) central…
The Casimir energy is the first-order-in-\hbar correction to the energy of a time-independent field configuration in a quantum field theory. We study the Casimir energy in a toy model, where the classical field is replaced by a separable…
This paper studies quantum field theories defined in networks, which are the multi-branch generalizations of interface conformal field theory (ICFT). We propose a novel junction condition on the node and show that it is consistent with…
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…
Non-trivial $\phi ^{4}$-theory is studied in a renormalisation group invariant approach inside a box consisting of rectangular plates and where the scalar modes satisfy periodic boundary conditions at the plates. It is found that the…
For renormalizable models a method is presented to unambiguously compute the energy that is carried by localized field configurations (solitons). A variational approach for the total energy is utilized to search for soliton configurations.…
We study the vacuum polarization (Casimir) energy in renormalizable, continuum quantum field theory in the presence of a background field, designed to impose Dirichlet boundary conditions on the fluctuating quantum field. In two and three…