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We invert the period map defined by the second structure connection of quantum cohomology of $\mathbb{P}^2$. For small quantum cohomology the inverse is given explicitly in terms of the Eisenstein series $E_4$ and $E_6$, while for big…
In this article a non--technical survey is given of the present status of Axiomatic Quantum Field Theory and interesting future directions of this approach are outlined. The topics covered are the universal structure of the local algebras…
The challenges posed by the development of field theories, both classical and quantum, force us to question their most basic and foundational ideas like the role and origin of space-time, the meaning of physical states, etc. Among them the…
In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by…
Several related operator-algebraic constructions for quantum field theory models on Minkowski spacetime are reviewed. The common theme of these constructions is that of a Borchers triple, capturing the structure of observables localized in…
Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are…
Several basic problems of the theory of quantum phase transitions are reviewed. The effect of the quantum correlations on the phase transition properties is considered with the help of basic models of statistical physics. The effect of…
Discussed is the structure of non-trivial counterterms that occur in the systematic gauge-invariant perturbation theory with unstable fields introduced in [hep-ph/9802307].
These lectures deal with selected aspects of quantum field theory in curved spacetime including the following topics: (1) Quantization of fields on a curved background, particle creation by gravitational fields, particle creation in an…
We explore perturbative double field theory about time-dependent (cosmological) backgrounds to cubic order. To this order the theory is consistent in a weakly constrained sense, so that for a toroidal geometry it encodes both momentum and…
In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker (FLRW) space-times arise as well-defined approximations to specific \emph{quantum} geometries. We initiate the development of a quantum theory of test scalar fields on these…
A generalized algebra of quantum observables, depending on extra dimensional constants, is considered. Some limiting forms of the algebra are investigated and their possible applications to the descriptions of interactions of fundamental…
A basic problem in quantizing a field in curved space is the decomposition of the classical modes in positive and negative frequency. The decomposition is equivalent to a choice of a complex structure in the space of classical solutions. In…
A quantum field theory generalization, Baaquie, of the Heath, Jarrow, and Morton (HJM) term structure model parsimoniously describes the evolution of imperfectly correlated forward rates. Field theory also offers powerful computational…
The logic--linguistic structure of quantum physics is analysed. The role of formal systems and interpretations in the representation of nature is investigated. The problems of decidability, completeness, and consistency can affect quantum…
This paper describes perturbative framework, on the basis of closed-time-path formalism, for studying quasiuniform relativistic quantum field systems near equilibrium and nonequilibrium quasistationary systems. At the first part, starting…
Two coalgebra structures are used in quantum field theory. The first one is the coalgebra part of a Hopf algebra leading to deformation quantization. The second one is a co-module co-algebra over the first Hopf algebra and it is used to…
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
Deformations of quantum field theories which preserve Poincar\'e covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an…
A rough overview is given over the most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory .