scholarly journals THERMOFIELD DYNAMICS FOR TWISTED POINCARÉ-INVARIANT FIELD THEORIES: WICK THEOREM AND S-MATRIX

2011 ◽  
Vol 26 (15) ◽  
pp. 2569-2589 ◽  
Author(s):  
MARCELO LEINEKER ◽  
AMILCAR R. QUEIROZ ◽  
ADEMIR E. SANTANA ◽  
CHRYSTIAN DE ASSIS SIQUEIRA
Keyword(s):  
Field Theory ◽  
Finite Temperature ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
S Matrix ◽  
Scalar Quantum ◽  
Wick Theorem ◽  
Wick’S Theorem ◽  
Invariant Quantum

Poincaré invariant quantum field theories can be formulated on noncommutative planes if the statistics of fields is twisted. This is equivalent to state that the coproduct on the Poincaré group is suitably twisted. In the present work we present a twisted Poincaré invariant quantum field theory at finite temperature. For that we use the formalism of thermofield dynamics (TFD). This TFD formalism is extend to incorporate interacting fields. This is a nontrivial step, since the separation in positive and negative frequency terms is no longer valid in TFD. In particular, we prove the validity of Wick's theorem for twisted scalar quantum field at finite temperature.

scholarly journals EXISTENCE OF ASYMPTOTIC EXPANSIONS IN NONCOMMUTATIVE QUANTUM FIELD THEORIES

2008 ◽  
Vol 20 (08) ◽  
pp. 933-949
Author(s):  
C. A. LINHARES ◽  
A. P. C. MALBOUISSON ◽  
I. RODITI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Asymptotic Behaviors ◽  
Scalar Quantum ◽  
Feynman Amplitudes ◽  
Mellin Representation ◽  
Noncommutative Quantum

Starting from the complete Mellin representation of Feynman amplitudes for noncommutative vulcanized scalar quantum field theory, introduced in a previous publication, we generalize to this theory the study of asymptotic behaviors under scaling of arbitrary subsets of external invariants of any Feynman amplitude. This is accomplished in both convergent and renormalized amplitudes.

scholarly journals Quantum Field Theory over $\mathbb{F}_q$

10.37236/589 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Oliver Schnetz
Keyword(s):  
Field Theory ◽  
Perturbation Series ◽  
The Other ◽  
Field Theories ◽  
Roots Of Unity ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Graph Hypersurfaces ◽  
Prime 2

We consider the number $\bar N(q)$ of points in the projective complement of graph hypersurfaces over $\mathbb{F}_q$ and show that the smallest graphs with non-polynomial $\bar N(q)$ have 14 edges. We give six examples which fall into two classes. One class has an exceptional prime 2 whereas in the other class $\bar N(q)$ depends on the number of cube roots of unity in $\mathbb{F}_q$. At graphs with 16 edges we find examples where $\bar N(q)$ is given by a polynomial in $q$ plus $q^2$ times the number of points in the projective complement of a singular K3 in $\mathbb{P}^3$. In the second part of the paper we show that applying momentum space Feynman-rules over $\mathbb{F}_q$ lets the perturbation series terminate for renormalizable and non-renormalizable bosonic quantum field theories.

scholarly journals Quantum computation of scattering in scalar quantum field theories

2014 ◽  
Vol 14 (11&12) ◽  
pp. 1014-1080 ◽  
Author(s):  
Stephen P. Jordan ◽  
Keith S. M. Lee ◽  
John Preskill
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Strong Coupling ◽  
Interaction Strength ◽  
Quantum Algorithm ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Scalar Quantum ◽  
Relativistic Scattering ◽  
Fundamental Physical

Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive $\phi^4$ theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling.

scholarly journals ON ALGEBRAIC STRUCTURES IMPLICIT IN TOPOLOGICAL QUANTUM FIELD THEORIES

1999 ◽  
Vol 08 (02) ◽  
pp. 125-163 ◽  
Author(s):  
Louis Crane ◽  
David Yetter
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hopf Algebra ◽  
Tensor Category ◽  
Topological Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Topological Quantum ◽  
Natural Way

We show that any 3D topological quantum field theory satisfying physically reasonable factorizability conditions has associated to it in a natural way a Hopf algebra object in a suitable tensor category. We also show that all objects in the tensor category have the structure of left-left crossed bimodules over the Hopf algebra object. For 4D factorizable topological quantum filed theories, we provide by analogous methods a construction of a Hopf algebra category.

Integrable Quantum Field Theories

2020 ◽  
pp. 575-621
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Conformal Theory ◽  
Integrable Quantum ◽  
Set Up ◽  
Integrable Quantum Field Theory

Chapter 16 covers the general properties of the integrable quantum field theories, including how an integrable quantum field theory is characterized by an infinite number of conserved charges. These theories are illustrated by means of significant examples, such as the Sine–Gordon model or the Toda field theories based on the simple roots of a Lie algebra. For the deformations of a conformal theory, it shown how to set up an efficient counting algorithm to prove the integrability of the corresponding model. The chapter focuses on two-dimensional models, and uses the term ‘two-dimensional’ to denote both a generic two-dimensional quantum field theory as well as its Euclidean version.

The Principles of Renormalisation

2021 ◽  
pp. 304-328
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Power Counting ◽  
Field Theories ◽  
Asymptotic Freedom ◽  
Green Functions ◽  
Quantum Field Theories ◽  
Quantum Field

Loop diagrams often yield ultraviolet divergent integrals. We introduce the concept of one-particle irreducible diagrams and develop the power counting argument which makes possible the classification of quantum field theories into non-renormalisable, renormalisable and super-renormalisable. We describe some regularisation schemes with particular emphasis on dimensional regularisation. The renormalisation programme is described at one loop order for φ‎4 and QED. We argue, without presenting the detailed proof, that the programme can be extended to any finite order in the perturbation expansion for every renormalisable (or super-renormalisable) quantum field theory. We derive the equation of the renormalisation group and explain how it can be used in order to study the asymptotic behaviour of Green functions. This makes it possible to introduce the concept of asymptotic freedom.

Estimates on Renormalization Group Transformations

1998 ◽  
Vol 50 (4) ◽  
pp. 756-793 ◽  
Author(s):  
D. Brydges ◽  
J. Dimock ◽  
T. R. Hurd
Keyword(s):  
Renormalization Group ◽  
Gaussian Measure ◽  
Ultra Violet ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
Scalar Quantum ◽  
Polymer Expansion ◽  
Renormalization Group Flows

AbstractWe consider a specific realization of the renormalization group (RG) transformation acting on functional measures for scalar quantum fields which are expressible as a polymer expansion times an ultra-violet cutoff Gaussian measure. The new and improved definitions and estimates we present are sufficiently general and powerful to allow iteration of the transformation, hence the analysis of complete renormalization group flows, and hence the construction of a variety of scalar quantum field theories.

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