Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Condition of causality in scattering theory

D. A. Slavnov

Published Jan 1, 1973• 0 citations
OpenAlex

Abstract

Within the framework of the scattering theory the principles of causality in the quantum field theory were formulated. The causality principles were stated in physical terms and occur both in relativistic and nonrelativistic theories. (tr-auth)

Related papers

Approach to nonrelativistic scattering theory, based on the principles of causality, superposition, and unitarity

R. Kh. Gainutdinov

The possibility of constructing a nonrelativistic scattering theory without appealing to the Schroedinger formalism is investigated, the theory being based on the general physical principles of causality, superposition, and unitarity. It is proved that the proposed approach is more general than the nonrelativistic scattering theory based on the Schroedinger equation. The proposed approach is used for the construction of a model scattering theory for a system consisting of heavy nonrelativistic particles and a light relativistic particle.

•Feb 1, 1983•0 citations

Causality and Analyticity in Formal Scattering Theory

Gerald N. Minerbo

The connection between causality and analyticity in scattering theory is formulated in terms of Hilbertspace concepts. The usual rules of nonrelativistic quantum mechanics are assumed to hold for the "in" and "out" states of the scattering system. We show that there is a (physically verifiable) causality condition which implies that each diagonal $S$-matrix element ${S}_{\ensuremath{\alpha}\ensuremath{\alpha}}(E)$ must be the limit of an analytic function of the energy $E$, regular in $\mathrm{Im}E>0$. The implications for partial-wave amplitudes and for the forward scattering amplitude in elastic two-body collisions are discussed.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Feb 15, 1971•6 citations

Causality and chance in relativistic quantum field theories

Richard Healey

Bell appealed to the theory of relativity in formulating his principle of local causality. But he maintained that quantum field theories do not conform to that principle, even when their field equations are relativistically covariant and their observable algebras satisfy a relativistically motivated microcausality condition. A pragmatist view of quantum theory and an interventionist approach to causation prompt the reevaluation of local causality and microcausality. Local causality cannot be understood as a reasonable requirement on relativistic quantum field theories: it is unmotivated even if applicable to them. But microcausality emerges as a sufficient condition for the consistent application of a relativistic quantum field theory.

arXiv:1405.3254•May 13, 2014•0 citations

Relativistic Causality in Algebraic Quantum Field Theory

John Earman, Giovanni Valente

This paper surveys the issue of relativistic causality within the framework of algebraic quantum field theory (AQFT). In doing so, we distinguish various notions of causality formulated in the literature and study their relationships, and thereby we offer what we hope to be a useful taxonomy. We propose that the most direct expression of relativistic causality in AQFT is captured not (as has sometimes been claimed) by the spectrum condition but rather by the axiom of local primitive causality, in that it entails a form of local determinism for quantum fields which generalizes the constraint of no superluminal propagation of classical field theories to relativistic quantum field theory. We discuss the status of the axiom of micro-causality by locating its place within a large family of separability/independence/locality conditions developed for AQFT and also by relating it to so-called no-signalling theorems. And we also provide a critical survey of attempts to understand the implications for relativistic causality of the distant correlations endemic to the states in models of AQFT satisfying the standard axioms, and we provide an assessment of attempts to employ Reichenbach's common cause principle in AQFT to defuse worries that these distant correlations implicate direct causal connections between relatively spacelike events.

International Studies in the Philosophy of Science•Jan 2, 2014•52 citations

Causality in Nonrelativistic Quantum Scattering

H. M. Nussenzveig

A new formulation of the causality condition, in terms of the total wave function at a finite distance from the scatterer, is given. This condition is employed to derive all known analytic properties of the scattering amplitude in both variables (energy and scattering angle or momentum transfer) for a scatterer of finite radius. It is shown that all the assumptions are valid in the particular case of scattering by a local potential. The relations between causality, Wigner's inequality, and completeness are discussed.

Physical Review•Jan 25, 1969•12 citations

Must the Microcausality Condition Be Interpreted Causally? Beyond Reduction and Matters of Fact

Jordi Cat

The 'microcausality' condition in quantum field theory is typically resented and justified on the basis of general principles of physical causality. I explore in detail a number of alternative causal interpretations of this condition. I conclude that none is fully satisfactory, independent of further and controversial assumptions about the object and scope of quantum field theories. In particular the stronger causal readings require a fully reductionist and fundamentalist attitude to quantum field theory. I argue, in a deflationary spirit, for a reading of the 'microcausality' condition as mere boundary condition, inspired by Relativity, that different possible formulations of quantum field theory must obey

•Jan 1, 2000•1 citation
The possibility of constructing a nonrelativistic scattering theory without appealing to the Schroedinger formalism is investigated, the theory being based on the general physical principles of causality, superposition, and unitarity. It is proved that the proposed approach is more general than the nonrelativistic scattering theory based on the Schroedinger equation. The proposed approach is used for the construction of a model scattering theory for a system consisting of heavy nonrelativistic particles and a light relativistic particle.
The connection between causality and analyticity in scattering theory is formulated in terms of Hilbertspace concepts. The usual rules of nonrelativistic quantum mechanics are assumed to hold for the "in" and "out" states of the scattering system. We show that there is a (physically verifiable) causality condition which implies that each diagonal SSS-matrix element ${S}_{\ensuremath{\alpha}\ensuremath{\alpha}}(E)$ must be the limit of an analytic function of the energy EEE, regular in ImE>0\mathrm{Im}E>0ImE>0. The implications for partial-wave amplitudes and for the forward scattering amplitude in elastic two-body collisions are discussed.
Bell appealed to the theory of relativity in formulating his principle of local causality. But he maintained that quantum field theories do not conform to that principle, even when their field equations are relativistically covariant and their observable algebras satisfy a relativistically motivated microcausality condition. A pragmatist view of quantum theory and an interventionist approach to causation prompt the reevaluation of local causality and microcausality. Local causality cannot be understood as a reasonable requirement on relativistic quantum field theories: it is unmotivated even if applicable to them. But microcausality emerges as a sufficient condition for the consistent application of a relativistic quantum field theory.
This paper surveys the issue of relativistic causality within the framework of algebraic quantum field theory (AQFT). In doing so, we distinguish various notions of causality formulated in the literature and study their relationships, and thereby we offer what we hope to be a useful taxonomy. We propose that the most direct expression of relativistic causality in AQFT is captured not (as has sometimes been claimed) by the spectrum condition but rather by the axiom of local primitive causality, in that it entails a form of local determinism for quantum fields which generalizes the constraint of no superluminal propagation of classical field theories to relativistic quantum field theory. We discuss the status of the axiom of micro-causality by locating its place within a large family of separability/independence/locality conditions developed for AQFT and also by relating it to so-called no-signalling theorems. And we also provide a critical survey of attempts to understand the implications for relativistic causality of the distant correlations endemic to the states in models of AQFT satisfying the standard axioms, and we provide an assessment of attempts to employ Reichenbach's common cause principle in AQFT to defuse worries that these distant correlations implicate direct causal connections between relatively spacelike events.
A new formulation of the causality condition, in terms of the total wave function at a finite distance from the scatterer, is given. This condition is employed to derive all known analytic properties of the scattering amplitude in both variables (energy and scattering angle or momentum transfer) for a scatterer of finite radius. It is shown that all the assumptions are valid in the particular case of scattering by a local potential. The relations between causality, Wigner's inequality, and completeness are discussed.
The 'microcausality' condition in quantum field theory is typically resented and justified on the basis of general principles of physical causality. I explore in detail a number of alternative causal interpretations of this condition. I conclude that none is fully satisfactory, independent of further and controversial assumptions about the object and scope of quantum field theories. In particular the stronger causal readings require a fully reductionist and fundamentalist attitude to quantum field theory. I argue, in a deflationary spirit, for a reading of the 'microcausality' condition as mere boundary condition, inspired by Relativity, that different possible formulations of quantum field theory must obey