Quaternionic Formulation of Supersymmetric Quantum Mechanics

Rawat, Seema; Negi, O. P. S.

doi:10.1007/s10773-008-9803-1

Cited by 15 publications

(10 citation statements)

References 12 publications

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“…According to hole theory absence of charge e with negative energy is equivalent to presence of positive energy operation, charge conjugation operation is = = ϯ (21) and = (22) where is quaternion conjugate and C is 4×4 matrix. Using equation ( 22) and equation (18) we get , so that…”

Section: A Invariance Of Quaternion Dirac Equation Under Charge Conjugationmentioning

confidence: 99%

CPT Invariance of Quaternion Dirac equation

Rawat¹

2022

IJRASET

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In this paper the invariance of Quaternion Dirac equation under Lorentz Transformation, Charge conjugation, Parity transformation and Time reversal operation has been discussed successfully. The invariance under the combined operation of Charge conjugation, Parity and Time reversal (CPT) has also been discussed and expression for C, P, T and combined CPT operators have been obtained in terms of quaternions. Invariance condition for electric and magnetic field has also been obtained. It has been concluded that the Quaternion Dirac equation dominates over ordinary Dirac equation because of the advantage of algebra of quaternions.

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Section: A Invariance Of Quaternion Dirac Equation Under Charge Conjugationmentioning

confidence: 99%

CPT Invariance of Quaternion Dirac equation

Rawat¹

2022

IJRASET

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“…The quaternions can be roughly characterized as an extension, involving three non-commuting imaginaries 2 similar to the familiar complex field. Since their discovery by Hamilton in 1843 and the pioneering work of Finkelstein, et.,al [6], quaternions have received a great deal of attention, e.g., [7,8,9,10,11,12,13,14,15], as a mathematical formalism for expressing physics. The most comprehensive and notable study of their applicability in quantum mechanics has been done by Adler [16].…”

Section: The Mathematical Structurementioning

confidence: 99%

A Possible Mathematical Structure for Physics

Welch

2009

Preprint

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The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings -the real, R, the complex, C, and the quaternion, H -known to meet the requirements of a mathematical description of our universe. The known forces and particle structure, in terms of families and color, can be associated with natural relationships within that structure. A "toy" scientific theory -based on the proposed mathematical structure -is presented to illustrate its applicability. It is shown how parity and time reversal invariance are broken. Two relevant predictions come from the formalism. First, there are no gravity waves and second, matter comes in three varieties, one of which is "dark" in the sense that it is oblivious to electromagnetic interactions. BackgroundThe relationship between mathematics and physics has been a matter of study since the time of the Pythagoreans. Notables such as Galilei, Hawking, Wheeler, and Wigner have pondered -to paraphrase each -"Why is mathematics so successful in describing the universe?" Recently Tegmark [1] has done an in depth study involving the tools of philosophy, mathematical descriptions, and physical systems to explore the relationship and to identify the requirements of a mathematical structure -such as computations and simulations -to represent physical reality and the reader is referred to his exhaustive set of references. Tegmark argues that "Our external physical reality is a mathematical universe" -the Mathematical Universe Hypothesis (MUH). Following his description Benioff [2] began the development of

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“…One possibility, is to sacrifice the assumption of locality or of "point" particles, as is done in string theories. A second possibility, which motivates the present work, is that a successful unification of the fundamental forces will require a generalization beyond complex quantum mechanics [1,2,3,4,5,6,7,8,9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%