Continuum regulation of the strong-coupling expansion for quantum field theory

1981 ◽  
Vol 24 (10) ◽  
pp. 2693-2705 ◽  
Author(s):  
Carl Bender ◽  
Fred Cooper ◽  
Richard Kenway ◽  
L. M. Simmons
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Strong Coupling ◽  
Strong Coupling Expansion ◽  
Quantum Field

scholarly journals Nonlocal Scalar Quantum Field Theory—Functional Integration, Basis Functions Representation and Strong Coupling Expansion

Particles ◽  
2019 ◽  
Vol 2 (3) ◽  
pp. 385-410 ◽  
Author(s):  
Matthew Bernard ◽  
Vladislav A. Guskov ◽  
Mikhail G. Ivanov ◽  
Alexey E. Kalugin ◽  
Stanislav L. Ogarkov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Strong Coupling ◽  
Functional Integration ◽  
Strong Coupling Expansion ◽  
Basis Functions ◽  
Model Parameters ◽  
Quantum Field ◽  
Primary Field ◽  
Coupling Constant

Nonlocal quantum field theory (QFT) of one-component scalar field φ in D-dimensional Euclidean spacetime is considered. The generating functional (GF) of complete Green functions Z as a functional of external source j, coupling constant g and spatial measure d μ is studied. An expression for GF Z in terms of the abstract integral over the primary field φ is given. An expression for GF Z in terms of integrals over the primary field and separable Hilbert space (HS) is obtained by means of a separable expansion of the free theory inverse propagator L ^ over the separable HS basis. The classification of functional integration measures D φ is formulated, according to which trivial and two nontrivial versions of GF Z are obtained. Nontrivial versions of GF Z are expressed in terms of 1-norm and 0-norm, respectively. In the 1-norm case in terms of the original symbol for the product integral, the definition for the functional integration measure D φ over the primary field is suggested. In the 0-norm case, the definition and the meaning of 0-norm are given in terms of the replica-functional Taylor series. The definition of the 0-norm generator Ψ is suggested. Simple cases of sharp and smooth generators are considered. An alternative derivation of GF Z in terms of 0-norm is also given. All these definitions allow to calculate corresponding functional integrals over φ in quadratures. Expressions for GF Z in terms of integrals over the separable HS, aka the basis functions representation, with new integrands are obtained. For polynomial theories φ 2 n , n = 2 , 3 , 4 , … , and for the nonpolynomial theory sinh 4 φ , integrals over the separable HS in terms of a power series over the inverse coupling constant 1 / g for both norms (1-norm and 0-norm) are calculated. Thus, the strong coupling expansion in all theories considered is given. “Phase transitions” and critical values of model parameters are found numerically. A generalization of the theory to the case of the uncountable integral over HS is formulated—GF Z for an arbitrary QFT and the strong coupling expansion for the theory φ 4 are derived. Finally a comparison of two GFs Z , one on the continuous lattice of functions and one obtained using the Parseval–Plancherel identity, is given.

Improvement of an Extrapolation Scheme for Strong-Coupling Expansion in Quantum Field Theory

1979 ◽  
Vol 43 (8) ◽  
pp. 537-540 ◽  
Author(s):  
Carl M. Bender ◽  
Fred Cooper ◽  
G. S. Guralnik ◽  
Ralph Roskies ◽  
David H. Sharp
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Strong Coupling ◽  
Strong Coupling Expansion ◽  
Quantum Field ◽  
Extrapolation Scheme

Strong-coupling expansion in quantum field theory

1979 ◽  
Vol 19 (6) ◽  
pp. 1865-1881 ◽  
Author(s):  
Carl M. Bender ◽  
Fred Cooper ◽  
G. S. Guralnik ◽  
David H. Sharp
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Strong Coupling ◽  
Strong Coupling Expansion ◽  
Quantum Field

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 PROOF OF TRIVIALITY OF λϕ4 THEORY

2007 ◽  
Vol 22 (13) ◽  
pp. 2433-2439 ◽  
Author(s):  
MARCO FRASCA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Harmonic Oscillator ◽  
Strong Coupling ◽  
Renormalization Constant ◽  
Strong Coupling Limit ◽  
Recent Analysis ◽  
Quantum Field ◽  
Yang Mills

We show that a recent analysis in the strong coupling limit of the λϕ4 theory proves that this theory is indeed trivial giving in this limit the expansion of a free quantum field theory. We can get in this way the propagator with the renormalization constant and the renormalized mass. As expected the theory in this limit has the same spectrum as a harmonic oscillator. Some comments about triviality of the Yang–Mills theory in the infrared are also given.

scholarly journals GREEN FUNCTIONS AND NONLINEAR SYSTEMS: SHORT TIME EXPANSION

2008 ◽  
Vol 23 (02) ◽  
pp. 299-308 ◽  
Author(s):  
MARCO FRASCA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Green Function ◽  
Strong Coupling Expansion ◽  
Green Functions ◽  
Quantum Field ◽  
Leading Order ◽  
Time Expansion ◽  
Higher Order Corrections ◽  
Short Time

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher-order corrections can be then computed giving a satisfactory agreement with numerical results. The relevance of these results relies on the possibility of fully exploiting a gradient expansion in both classical and quantum field theory granting the existence of a strong coupling expansion. Having a Green function in this regime in quantum field theory amounts to obtain the corresponding spectrum of the theory.

EXACT DUALITY BETWEEN INTEGRABLE DEFORMATIONS OF BCn AND $C_n^{(1)}$ AFFINE TODA THEORIES

1998 ◽  
Vol 13 (12) ◽  
pp. 937-951 ◽  
Author(s):  
P. BASEILHAC ◽  
P. GRANGÉ ◽  
V. A. FATEEV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Strong Coupling ◽  
Field Theories ◽  
Quantum Field ◽  
Coupling Constant ◽  
Perturbative Calculations ◽  
Quantum Integrability ◽  
Integrable Deformations

Integrable deformations of two affine Toda field theories based on BCn and [Formula: see text] non-simply laced algebras are studied. The proof of quantum integrability of the two theories is given and it is shown that the two theories are dual, corresponding respectively to the weak and strong coupling regimes of an intermediate theory. Perturbative calculations and the bootstrap principle permit the construction of the intermediate quantum field theory which flows from the first to the second with the coupling constant.

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