## Extension of the Algebra of Poincare Group Generators and Violation of p Invariance in JETP Letters: A Translation of JETP Pis’ma v Redaktsiyu of the Academy of Sciences of the USSR, 13, No. 8, April 20, 1971 pp. 323–326

RARE FIRST EDITION IN ORIGINAL WRAPS of the paper which pioneered the modern concept of what would later become known as supersymmetry. (A supersymmetry relating mesons and baryons was proposed by Miyazawa in 1966, but did not involve spacetime and was largely ignored). Gol’fand and Likhtman’s 1971 work is “the first paper on (relativistic) spacetime supersymmetry” (Baer, Weak Scale Supersymmetry: 3.1a). In particle physics, Supersymmetry as a proposed type of spacetime symmetry relates two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin (Haber, Supersymmetry, Part I, PDG, 8 July 2015). Involving Fermi-Bose symmetry transformation, at the level of quantum mechanics, suypersymmetry employs a quantum operator – or a Q – whose job is to turn bosons into fermions and vice versa.

While supersymmetry is now integral to particle physics research, it is interesting to note that this was in no way the intent or subject of Folfand and Likhtman’s paper. “Rather than trying to add fermions to a bosonic theory, they were exploring the mathematics of space-time with the primary motivation to do something exotic with the group theory of spacetime symmetries.

“The usual group of spacetime symmetries in relativistic quantum field theory is called the Poincare' group. This group includes symmetries under spatial rotations, spacetime boosts and translations in space and time. The action of the group can be described by the algebra of the group, which is defined by a set of commutation relations between the generators of infinitesimal group transformations. These are all bosonic symmetries, which ought to be so because momentum conservation and Lorentz invariance are present in classical physics.

“But the Poincare' group also has representations that describe fermions. Since spin 1/2 particles arise as solutions to a relativistically invariant equation -- the Dirac equation -- this is to be expected. If there are spin 1/2 particles, could there be spin 1/2 symmetry generators in a spacetime symmetry algebra? Yes! By introducing such symmetry generators Gol’fand and Likhtman have constructed the first example of supercharges mentioned above. What Gol'fand and Likhtman ended up with was the group theory of supersymmetric transformations in four spacetime dimensions, and using this new type of symmetry, they constructed the first supersymmetric quantum field theory” (JETP Letters, 12/29/2013). Item #623

CONDITION & DETAILS: Individual issue in original wraps. Lancaster, Pennsylvania: American Institute of Physics. 4to (11 x 8.5; 275 x 213mm). Ex-libris with stamp on front wrap (see scan) and no other markings whatsoever. Near fine condition – clean, bright, and tightly bound.

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Price:
$700.00
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