scholarly journals Scalar quantum field theories as a benchmark for near-term quantum computers

2019 ◽  
Vol 99 (3) ◽  
Author(s):  
Kübra Yeter-Aydeniz ◽  
Eugene F. Dumitrescu ◽  
Alex J. McCaskey ◽  
Ryan S. Bennink ◽  
Raphael C. Pooser ◽  
...  
Keyword(s):  
Field Theories ◽  
Quantum Computers ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Scalar Quantum ◽  
Near Term

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.

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 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 Anti-Newtonian Expansions and the Functional Renormalization Group

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 85 ◽  
Author(s):  
Max Niedermaier
Keyword(s):  
Renormalization Group ◽  
Degrees Of Freedom ◽  
World Line ◽  
Newtonian Limit ◽  
Field Theories ◽  
Quantum Mechanical ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Functional Renormalization Group ◽  
Scalar Quantum

Anti-Newtonian expansions are introduced for scalar quantum field theories and classical gravity. They expand around a limiting theory that evolves only in time while the spatial points are dynamically decoupled. Higher orders of the expansion re-introduce spatial interactions and produce overlapping lightcones from the limiting isolated world line evolution. In scalar quantum field theories, the limiting system consists of copies of a self-interacting quantum mechanical system. In a spatially discretized setting, a nonlinear “graph transform” arises that produces an in principle exact solution of the Functional Renormalization Group for the Legendre effective action. The quantum mechanical input data can be prepared from its 1 + 0 dimensional counterpart. In Einstein gravity, the anti-Newtonian limit has no dynamical spatial gradients, yet remains fully diffeomorphism invariant and propagates the original number of degrees of freedom. A canonical transformation (trivialization map) is constructed, in powers of a fractional inverse of Newton’s constant, that maps the ADM action into its anti-Newtonian limit. We outline the prospects of an associated trivializing flow in the quantum theory.

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