scholarly journals Regularization of ultraviolet divergence for a particle interacting with a scalar quantum field

2015 ◽  
Vol 92 (12) ◽  
Author(s):  
O. D. Skoromnik ◽  
I. D. Feranchuk ◽  
D. V. Lu ◽  
C. H. Keitel
Keyword(s):  
Ultraviolet Divergence ◽  
Quantum Field ◽  
Scalar Quantum

scholarly journals Thermal Casimir effect with general boundary conditions

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
J. M. Muñoz-Castañeda ◽  
L. Santamaría-Sanz ◽  
M. Donaire ◽  
M. Tello-Fraile
Keyword(s):  
Boundary Conditions ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
Quantum Field ◽  
Quantum Vacuum ◽  
Parallel Plates ◽  
Casimir Forces ◽  
Thermal Correction ◽  
Frequency Independent ◽  
Scalar Quantum

Abstract In this paper we study the system of a scalar quantum field confined between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium. We represent the plates by the most general lossless and frequency-independent boundary conditions that satisfy the conditions of isotropy and homogeneity and are compatible with the unitarity of the quantum field theory. Under these conditions we compute the thermal correction to the quantum vacuum energy as a function of the temperature and the parameters encoding the boundary condition. The latter enables us to obtain similar results for the pressure between plates and the quantum thermal correction to the entropy. We find out that our system is thermodynamically stable for any boundary conditions, and we identify a critical temperature below which certain boundary conditions yield attractive, repulsive, and null Casimir forces.

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.

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 Perturbation Theory of Transformed Quantum Fields

2020 ◽  
Vol 23 (3) ◽  
Author(s):  
Paul-Hermann Balduf
Keyword(s):  
Perturbation Theory ◽  
Path Integral ◽  
Field Variable ◽  
Quantum Field ◽  
Arbitrary Polynomial ◽  
Free Theory ◽  
Scalar Quantum ◽  
Additional Interaction ◽  
The One ◽  
Quadratic Order

Abstract We consider a scalar quantum field ϕ with arbitrary polynomial self-interaction in perturbation theory. If the field variable ϕ is repaced by a global diffeomorphism ϕ(x) = ρ(x) + a1ρ2(x) + …, this field ρ obtains infinitely many additional interaction vertices. We propose a systematic way to compute connected amplitudes for theories involving vertices which are able to cancel adjacent edges. Assuming tadpole graphs vanish, we show that the S-matrix of ρ coincides with the one of ϕ without using path-integral arguments. This result holds even if the underlying field has a propagator of higher than quadratic order in the momentum. The diffeomorphism can be tuned to cancel all contributions of an underlying ϕt-type self interaction at one fixed external offshell momentum, rendering ρ a free theory at this momentum. Finally, we mention one way to extend the diffeomorphism to a non-diffeomorphism transformation involving derivatives without spoiling the combinatoric structure of the global diffeomorphism.

scholarly journals No resonant tunneling in standard scalar quantum field theory

2008 ◽  
Vol 2008 (01) ◽  
pp. 066-066 ◽  
Author(s):  
Edmund J Copeland ◽  
Antonio Padilla ◽  
Paul M Saffin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Resonant Tunneling ◽  
Quantum Field ◽  
Scalar Quantum
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