80 Years of Professor Wigner's Seminal Work "On Unitary Representations of the Inhomogeneous Lorentz Group"

By E. Wigner. 2021

2,014 citations recorded by the source corpus.

It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally represented by wave functions3 in such a way that φ and constant multiples of φ represent the same physical state. It is possible, therefore, to normalize the wave function, i.e., to multiply it by a constant factor such that its scalar product with itself becomes 1. Then, only a constant factor of modulus 1, the so-called phase, will be left undetermined in the wave function. The linear character of the wave function is called the superposition principle. The square of the modulus of the unitary scalar product (ψ,Φ) of two normalized wave functions ψ and Φ is called the transition probability from the state ψ into Φ, or conversely. This is supposed to give the probability that an experiment performed on a system in the state Φ, to see whether or not the state is ψ, gives the result that it is ψ. If there are two or more different experiments to decide this (e.g., essentially the same experiment, performed at different times) they are all supposed to give the same result, i.e., the transition probability has an invariant physical sense.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e7a88a5d0617b5adbefcedccb5e52a12725de6bf

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Citations in the corpus

Notes on the BMS group in three dimensions: I. Induced representations (2014, background): “The origin of these general group-theoretic results is the celebrated work by Wigner [43] on the classification of the irreducible representations of the Poincaré group.”
Quantum Information and Relativity Theory (2002, background): “The reason is that under a Lorentz boost, the spin undergoes a Wigner rotation (Wigner, 1939; Halpern, 1968) whose direction and magnitude depend on the momentum of the particle.”
Amplitudes and Spinor-Helicity in Six Dimensions (2009, background): “This reflects a very basic result from field theory: asymptotic states of zero mass are uniquely specified by their momentum and helicity, and as such the S-matrix should be a function of these variables alone [1, 2].”
Spin-half fermions with mass dimension one: theory, phenomenology, and dark matter (2004, background): “be viewed with dark matter and modiﬁcations of gravity at large scales as complimentary contributors to the same data. From a formal theoretical point of view, building on the classic works of Wigner [6,19], this paper provides an account of our attempt to understand the particle content as implied ”