Determination of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Σ</mml:mi><mml:mo>−</mml:mo><mml:mi>Λ</mml:mi></mml:math>Relative Parity

Alff, C.; Gelfand, N.; Nauenberg, U.; Nussbaum, M.; Schultz, J.; Steinberger, J.; Brugger, H.; Kirsch, L.; Plano, R. J.; Berley, D.; Prodell, A.

doi:10.1103/physrev.137.b1105

Cited by 19 publications

(22 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…equations which can be used to distinguish Pin(3,1) and Pin (3,1). We note that P (3) is P (1) followed by a rotation; Λ 2 P (3) is Λ 2 P (1) followed by the effect of a 2π rotation on the pinor, hence Λ 2…”

Section: Pin(31)mentioning

confidence: 99%

“…Since Spin (1,3) and Spin(3,1) are isomorphic, the differences between Pin(1,3) and Pin(3,1) appear only in discussions of space or time reversals. Λ P , Λ T are not in Spin(1,3) but Λ 2 P and Λ…”

Section: A Spin Group Is a Subgroup Of A Pin Groupmentioning

confidence: 99%

“…Spin (1,3) consists of even elements (products of an even number of γ α ) of Pin (1,3). Spin(1,3) is isomorphic to Spin(3,1), but Pin(1,3) is not isomorphic to Pin (3,1).…”

Section: A Spin Group Is a Subgroup Of A Pin Groupmentioning

confidence: 99%

“…• Pin (3,1) 3.2 A Spin group is a subgroup of a Pin group 3.3 Pin group and Spin group representations on finite-dimensional spaces; classical fields.…”

Section: The Pin Groupsmentioning

confidence: 99%

“…Whereas there is, up to an isomorphism, only one Spin group which double covers the orientation preserving Lorentz group, there are two essentially different groups, called Pin groups, which cover the full Lorentz group. The name Pin is gaining acceptance because it is a useful name: Pin(1,3) is to O (1,3) what Spin(1,3) is to SO (1,3). The existence of two Pin groups explains several issues which we discuss in section 2.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The Pin Groups in Physics: C, P and T

et al. 2001

View full text Add to dashboard Cite

A simple, but not widely known, mathematical fact concerning the coverings of the full Lorentz group sheds light on parity and time reversal transformations of fermions. Whereas there is, up to an isomorphism, only one Spin group which double covers the orientation preserving Lorentz group, there are two essentially different groups, called Pin groups, which cover the full Lorentz group. Pin(1,3) is to O (1,3) what Spin(1,3) is to SO (1,3). The existence of two Pin groups offers a classification of fermions based on their properties under space or time reversal finer than the classification based on their properties under orientation preserving Lorentz transformations -provided one can design experiments that distinguish the two types of fermions. Many promising experimental setups give, for one reason or another, identical results for both types of fermions. These negative results are reported here because they are instructive. Two notable positive results show that the existence of two Pin groups is relevant to physics:• In a neutrinoless double beta decay, the neutrino emitted and reabsorbed in the course of the interaction can only be described in terms of Pin(3,1).• If a space is topologically nontrivial, the vacuum expectation values of Fermi currents defined on this space can be totally different when described in terms of Pin(1,3) and Pin(3,1).Possibly more important than the two above predictions, the Pin groups provide a simple framework for the study of fermions; it makes possible clear definitions of intrinsic parities and time reversal; it clarifies colloquial, but literally meaningless, statements. Given the difference between the Pin group and the Spin group it is useful to distinguish their representations, as groups of transformations on "pinors" and "spinors", respectively.The Pin(1,3) and Pin(3,1) fermions are twin-like particles whose behaviors differ only under space or time reversal.A section on Pin groups in arbitrary spacetime dimensions is included.

show abstract

Section: Pin(31)mentioning

confidence: 99%

Section: A Spin Group Is a Subgroup Of A Pin Groupmentioning

confidence: 99%

“…Spin (1,3) consists of even elements (products of an even number of γ α ) of Pin (1,3). Spin(1,3) is isomorphic to Spin(3,1), but Pin(1,3) is not isomorphic to Pin (3,1).…”

Section: A Spin Group Is a Subgroup Of A Pin Groupmentioning

confidence: 99%

“…• Pin (3,1) 3.2 A Spin group is a subgroup of a Pin group 3.3 Pin group and Spin group representations on finite-dimensional spaces; classical fields.…”

Section: The Pin Groupsmentioning

confidence: 99%