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.

scholarly journals Logarithmic expansion of field theories: higher orders and resummations

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Vincenzo Branchina ◽  
Alberto Chiavetta ◽  
Filippo Contino
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Order ◽  
Weak Coupling ◽  
Field Theories ◽  
Quantum Field ◽  
First Order ◽  
Free Theory ◽  
Formal Expansion ◽  
The Way

AbstractA formal expansion for the Green’s functions of a quantum field theory in a parameter $$\delta $$ δ that encodes the “distance” between the interacting and the corresponding free theory was introduced in the late 1980s (and recently reconsidered in connection with non-hermitian theories), and the first order in $$\delta $$ δ was calculated. In this paper we study the $${\mathcal {O}}(\delta ^2)$$ O ( δ 2 ) systematically, and also push the analysis to higher orders. We find that at each finite order in $$\delta $$ δ the theory is non-interacting: sensible physical results are obtained only resorting to resummations. We then perform the resummation of UV leading and subleading diagrams, getting the $${\mathcal {O}}(g)$$ O ( g ) and $${\mathcal {O}}(g^2)$$ O ( g 2 ) weak-coupling results. In this manner we establish a bridge between the two expansions, provide a powerful and unique test of the logarithmic expansion, and pave the way for further studies.

scholarly journals A novel view on successive quantizations, leading to increasingly more “miraculous” states

2019 ◽  
Vol 34 (23) ◽  
pp. 1950186 ◽  
Author(s):  
Matej Pavšič
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Function ◽  
Wave Packet ◽  
Time Derivative ◽  
Point Particle ◽  
Order Equation ◽  
Quantum Field ◽  
First Order ◽  
Complex Wave

A series of successive quantizations is considered, starting with the quantization of a non-relativistic or relativistic point particle: (1) quantization of a particle’s position, (2) quantization of wave function, (3) quantization of wave functional. The latter step implies that the wave packet profiles forming the states of quantum field theory are themselves quantized, which gives new physical states that are configurations of configurations. In the procedure of quantization, instead of the Schrödinger first-order equation in time derivative for complex wave function (or functional), the equivalent second-order equation for its real part was used. In such a way, at each level of quantization, the equation a quantum state satisfies is just like that of a harmonic oscillator, and wave function(al) is composed in terms of the pair of its canonically conjugated variables.

scholarly journals 𝒫𝒯-symmetric quantum field theory on the noncommutative spacetime

2019 ◽  
Vol 35 (05) ◽  
pp. 2050012
Author(s):  
Oleg O. Novikov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitude ◽  
Quantum Field ◽  
Leading Order ◽  
Symmetric Quantum ◽  
Noncommutative Spacetime ◽  
T Matrix ◽  
The One ◽  
New Formula

We consider the [Formula: see text]-symmetric quantum field theory on the noncommutative spacetime with angular twist and construct its pseudo-Hermitian interpretation. We explore the differences between internal and spatial parities in the context of the angular twist and for the latter we find new [Formula: see text]-symmetric interactions that are nontrivial only for the noncommutative spacetime. We reproduce the same formula for the leading order T-matrix of the equivalent Hermitian model as the one obtained earlier for the quantum field theory on the commutative spacetime. This formula implies that the leading order scattering amplitude preserves the symmetries of the noncommutative geometry if they are not broken in the non-Hermitian formulation.

scholarly journals Quantum Ostrogradsky theorem

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Hayato Motohashi ◽  
Teruaki Suyama
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
First Order ◽  
Higher Derivative ◽  
Original Theorem ◽  
Classical Lagrangian

Abstract The Ostrogradsky theorem states that any classical Lagrangian that contains time derivatives higher than the first order and is nondegenerate with respect to the highest-order derivatives leads to an unbounded Hamiltonian which linearly depends on the canonical momenta. Recently, the original theorem has been generalized to nondegeneracy with respect to non-highest-order derivatives. These theorems have been playing a central role in construction of sensible higher-derivative theories. We explore quantization of such non-degenerate theories, and prove that Hamiltonian is still unbounded at the level of quantum field theory.

scholarly journals DUALITY OF STRING AMPLITUDES IN A CURVED BACKGROUND

1993 ◽  
Vol 08 (30) ◽  
pp. 5409-5440
Author(s):  
MÅNS HENNINGSON
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitudes ◽  
String Theory ◽  
Target Space ◽  
Quantum Field ◽  
Group Manifold ◽  
String Amplitudes ◽  
Theory Calculation ◽  
The Relationship

We initiate a program to study the relationship between the target space, the spectrum and the scattering amplitudes in string theory. We consider scattering amplitudes following from string theory and quantum field theory on a curved target space, which is taken to be the SU(2) group manifold, with special attention given to the duality between contributions from different channels. We give a simple example of the equivalence between amplitudes coming from string theory and quantum field theory, and compute the general form of a four-scalar field-theoretical amplitude. The corresponding string theory calculation is performed for a special case, and we discuss how more general string theory amplitudes could be evaluated.

A twistor approach to the regularization of divergences

1985 ◽  
Vol 397 (1813) ◽  
pp. 341-374 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Infrared Divergence ◽  
Standard Theory ◽  
Quantum Field ◽  
New Formalism ◽  
First Order ◽  
Finite Theory ◽  
Finite Quantity ◽  
Modified Theory

One object of the twistor programme, as developed principally by R. Penrose, is the production of a manifestly finite theory of scattering in quantum field theory. Earlier work has shown that progress towards this goal is obstructed even at the first-order level, by the appearance of an infrared divergence in the standard theory. New studies in many-dimensional contour integration now suggest a simple but very powerful modification to this branch of twistor theory, in which the full (as opposed to the projective) twistor space plays an essential role. In this modified theory there arise natural contour-integral expressions with the effect of eliminating the infrared divergence previously noted, and replacing it by a finite quantity. This regularization can be specified by using a formalism of ‘inhomogeneous twistor diagrams’. The interpretation of this new formalism is not yet wholly clear, but the inhomogeneity can be seen as a means of relinquishing the concept of space-time point, while preserving light-cone structure. It therefore suggests a quite fresh approach to the divergences of quantum field theory.

Introduction to scattering amplitudes

2019 ◽  
pp. 183-204
Author(s):  
David A. Kosower
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitudes ◽  
Traditional Approach ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
The Past

This chapter covers the new on-shell methods that have been developed over the past twenty years for computing scattering amplitudes in quantum field theory. These methods break free from the traditional approach of Feynman diagrams. The chapter covers a subset of topics, setting up the basic kinematics, spinor helicities, spinor products, and the calculation of tree amplitudes.

scholarly journals On the singular behaviour of scattering amplitudes in quantum field theory

2014 ◽  
Vol 2014 (11) ◽  
Author(s):  
Sebastian Buchta ◽  
Grigorios Chachamis ◽  
Petros Draggiotis ◽  
Ioannis Malamos ◽  
Germán Rodrigo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitudes ◽  
Quantum Field ◽  
Singular Behaviour
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