Minkowski space

Summary

In mathematical physics, Minkowski space (or Minkowski spacetime) (mɪŋˈkɔːfski,_-ˈkɒf-) combines inertial space and time manifolds (x,y) with a non-inertial reference frame of space and time (x',t') into a four-dimensional model relating a position (inertial frame of reference) to the field (physics). A four-vector (x,y,z,t) consists of a coordinate axes such as a Euclidean space plus time. This may be used with the non-inertial frame to illustrate specifics of motion, but should not be confused with the spacetime model generally. The model helps show how a spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Mathematician Hermann Minkowski developed it from the work of Hendrik Lorentz, Henri Poincaré, and others, and said it "was grown on experimental physical grounds." Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical s

Official source

https://en.wikipedia.org/wiki/Minkowski_space

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Minkowski space is locally the Noldus limit of Poisson process causets

Jan Cristina

A Poisson process P-lambda on R-d with causal structure inherited from the the usual Minkowski metric on R-d has a normalised discrete causal distance D-lambda (x, y) given by the height of the longest causal chain normalised by lambda(1/d)c(d). We prove that P-lambda restricted to a compact set Q converges in probability in the sense of Noldus (2004 Class. Quantum Grav. 21 839-50) to Q with the Minkowski metric.

Iop Publishing Ltd2016

4D CFTs have a scale anomaly characterized by the coefficient c, which appears as the coefficient of logarithmic terms in momentum space correlation functions of the energy-momentum tensor. By studying the CFT contribution to 4-point graviton scattering amplitudes in Minkowski space we derive a sum rule for c in terms of TTO OPE coefficients. The sum rule can be thought of as a version of the optical theorem, and its validity depends on the existence of the massless and forward limits of the < TTTT > correlation functions that contribute. The finiteness of these limits is checked explicitly for free scalar, fermion, and vector CFTs. The sum rule gives c as a sum of positive terms, and therefore implies a lower bound on c given any lower bound on TTO OPE coefficients. We compute the coefficients to the sum rule for arbitrary operators of spin 0 and 2, including the energy-momentum tensor.

SPRINGER2018

In conformal field theory in Minkowski momentum space, the 3-point correlation functions of local operators are completely fixed by symmetry. Using Ward identities together with the existence of a Lorentzian operator product expansion (OPE), we show that the Wightman function of three scalar operators is a double hypergeometric series of the Appell F-4 type. We extend this simple closed-form expression to the case of two scalar operators and one traceless symmetric tensor with arbitrary spin. Time-ordered and partially-time-ordered products are constructed in a similar fashion and their relation with the Wightman function is discussed.

SPRINGER2020