Variance method in quantum field theory and exact strong-coupling limit of the Gaussian effective potential

1992 ◽  
Vol 54 (2) ◽  
pp. 297-306
Author(s):  
Uwe Ritschel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Strong Coupling ◽  
Effective Potential ◽  
Strong Coupling Limit ◽  
Quantum Field ◽  
Variance Method ◽  
Gaussian Effective Potential

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.

THE UNCERTAINTY OF THE GAUSSIAN EFFECTIVE POTENTIAL

1988 ◽  
Vol 03 (09) ◽  
pp. 2143-2163 ◽  
Author(s):  
R. MUÑOZ-TAPIA ◽  
J. TARON ◽  
R. TARRACH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Effective Potential ◽  
Anharmonic Oscillator ◽  
Liouville Theory ◽  
Quantum Field ◽  
First Case ◽  
Gaussian Effective Potential

An uncertainty is introduced for the Gaussian Effective Potential. The definition is quite straightforward for quantum mechanics but fairly subtle for quantum field theory. The uncertainty provides a good estimation of the error in the first case, but renormalization seems to spoil its usefulness in the second case. The examples considered are the anharmonic oscillator, λϕ4 in 3+1 dimensions and the Liouville theory in 1+1 dimensions.

scholarly journals GREEN FUNCTION METHOD FOR NONLINEAR SYSTEMS

2007 ◽  
Vol 22 (18) ◽  
pp. 1293-1299 ◽  
Author(s):  
MARCO FRASCA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Green Function ◽  
Nonlinear Systems ◽  
Strong Coupling ◽  
Function Method ◽  
Strong Coupling Limit ◽  
Quantum Field ◽  
Green Function Method ◽  
Function Solution

We show that a Green function solution can be given for a class of nonhomogeneous nonlinear systems having relevance in quantum field theory. This in turn means that a quantum field theory in the strong coupling limit can be formulated and the spectrum obtained.

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 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.

scholarly journals Fixing the non-relativistic expansion of the 1PM potential

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Gianluca Grignani ◽  
Troels Harmark ◽  
Marta Orselli ◽  
Andrea Placidi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitudes ◽  
Canonical Transformation ◽  
Effective Potential ◽  
Scattering Amplitude ◽  
Quantum Field ◽  
First Order ◽  
Scalar Matter ◽  
Frame Dependence

Abstract We obtain a first order post-Minkowskian two-body effective potential whose post-Newtonian expansion directly reproduces the Einstein-Infeld-Hoffmann potential. Post-Minkowskian potentials can be extracted from on-shell scattering amplitudes in a quantum field theory of scalar matter coupled to gravity. Previously, such potentials did not reproduce the Einstein-Infeld-Hoffmann potential without employing a suitable canonical transformation. In this work, we resolve this issue by obtaining a new expression for the first-order post-Minkowskian potential. This is accomplished by exploiting the reference frame dependence that arises in the scattering amplitude computation. Finally, as a check on our result, we demonstrate that our new potential gives the correct scattering angle.

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