Generalized unitary evolution for symplectic scalar fermions
A bstract The theory of symplectic scalar fermion of LeClair and Neubert is studied. The theory evades the conventional spin-statistics theorem because its Hamiltonian is pseudo Hermitian. The definition of pseudo Hermiticity is examined in the interacting and the Heisenberg picture. For states that...
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| Published in | The journal of high energy physics Vol. 2024; no. 5; pp. 181 - 19 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
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15.05.2024
Springer Nature B.V SpringerOpen |
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| Abstract | A
bstract
The theory of symplectic scalar fermion of LeClair and Neubert is studied. The theory evades the conventional spin-statistics theorem because its Hamiltonian is pseudo Hermitian. The definition of pseudo Hermiticity is examined in the interacting and the Heisenberg picture. For states that evolve under pseudo Hermitian Hamiltonians, we define the appropriate inner-product and matrix element of operators that preserve time translation symmetry. The resulting
S
-matrix is shown to satisfy the generalized unitarity relation. We clarify the derivation of the symplectic currents and charges. By demanding the currents and charges to be pseudo Hermitian, the global symmetry of the free Lagrangian density reduces from Sp(2, ℂ) to SU(2). By explicit calculations, we show that the LeClair-Neubert model of
N
quartic self-interacting scalar fermions admits generalized unitary evolution. |
|---|---|
| AbstractList | The theory of symplectic scalar fermion of LeClair and Neubert is studied. The theory evades the conventional spin-statistics theorem because its Hamiltonian is pseudo Hermitian. The definition of pseudo Hermiticity is examined in the interacting and the Heisenberg picture. For states that evolve under pseudo Hermitian Hamiltonians, we define the appropriate inner-product and matrix element of operators that preserve time translation symmetry. The resulting S -matrix is shown to satisfy the generalized unitarity relation. We clarify the derivation of the symplectic currents and charges. By demanding the currents and charges to be pseudo Hermitian, the global symmetry of the free Lagrangian density reduces from Sp(2, ℂ) to SU(2). By explicit calculations, we show that the LeClair-Neubert model of N quartic self-interacting scalar fermions admits generalized unitary evolution. A bstract The theory of symplectic scalar fermion of LeClair and Neubert is studied. The theory evades the conventional spin-statistics theorem because its Hamiltonian is pseudo Hermitian. The definition of pseudo Hermiticity is examined in the interacting and the Heisenberg picture. For states that evolve under pseudo Hermitian Hamiltonians, we define the appropriate inner-product and matrix element of operators that preserve time translation symmetry. The resulting S -matrix is shown to satisfy the generalized unitarity relation. We clarify the derivation of the symplectic currents and charges. By demanding the currents and charges to be pseudo Hermitian, the global symmetry of the free Lagrangian density reduces from Sp(2, ℂ) to SU(2). By explicit calculations, we show that the LeClair-Neubert model of N quartic self-interacting scalar fermions admits generalized unitary evolution. Abstract The theory of symplectic scalar fermion of LeClair and Neubert is studied. The theory evades the conventional spin-statistics theorem because its Hamiltonian is pseudo Hermitian. The definition of pseudo Hermiticity is examined in the interacting and the Heisenberg picture. For states that evolve under pseudo Hermitian Hamiltonians, we define the appropriate inner-product and matrix element of operators that preserve time translation symmetry. The resulting S-matrix is shown to satisfy the generalized unitarity relation. We clarify the derivation of the symplectic currents and charges. By demanding the currents and charges to be pseudo Hermitian, the global symmetry of the free Lagrangian density reduces from Sp(2, ℂ) to SU(2). By explicit calculations, we show that the LeClair-Neubert model of N quartic self-interacting scalar fermions admits generalized unitary evolution. |
| ArticleNumber | 181 |
| Author | Lee, Cheng-Yang |
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| References | W. Pauli, On Dirac’s New Method of Field Quantization, Rev. Mod. Phys.15 (1943) 175. DasDDasSRJevickiAYeQBi-local Construction of Sp(2N)/dS Higher Spin CorrespondenceJHEP2013011072013JHEP...01..107D304550810.1007/JHEP01(2013)107[arXiv:1205.5776] [INSPIRE] AhluwaliaDVda SilvaJMHLeeC-YMass dimension one fields with Wigner degeneracy: A theory of dark matterNucl. Phys. B2023987116092454190010.1016/j.nuclphysb.2023.116092[arXiv:2212.13114] [INSPIRE] AnninosDHartmanTStromingerAHigher Spin Realization of the dS/CFT CorrespondenceClass. Quant. Grav.2017342017CQGra..34a5009A359614110.1088/1361-6382/34/1/015009[arXiv:1108.5735] [INSPIRE] BenderCMMaking sense of non-Hermitian HamiltoniansRept. Prog. Phys.2007709472007RPPh...70..947B233129410.1088/0034-4885/70/6/R03[hep-th/0703096] [INSPIRE] Y. Nambu and G. Jona-Lasinio, Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. 1, Phys. Rev.122 (1961) 345 [INSPIRE]. MostafazadehAPseudo-Hermitian Representation of Quantum MechanicsInt. J. Geom. Meth. Mod. Phys.201071191274938510.1142/S0219887810004816[arXiv:0810.5643] [INSPIRE] D.V. Ahluwalia and C.-Y. Lee, Spin-half bosons with mass dimension three-half: Evading the spin-statistics theorem, EPL140 (2022) 24001 [Erratum ibid.140 (2022) 69901] [arXiv:2212.09457] [INSPIRE]. C.M. Bender and S. Boettcher, Real spectra in nonHermitian Hamiltonians having PT symmetry, Phys. Rev. Lett.80 (1998) 5243 [physics/9712001] [INSPIRE]. RyuSYoonJUnitarity of Symplectic Fermions in α Vacua with Negative Central ChargePhys. Rev. Lett.20231302416022023PhRvL.130x1602R460898310.1103/PhysRevLett.130.241602[arXiv:2208.12169] [INSPIRE] P.A.M. Dirac, Quantised singularities in the electromagnetic field, Proc. Roy. Soc. Lond. A133 (1931) 60 [INSPIRE]. A. Mostafazadeh, PseudoHermiticity versus PT symmetry. The necessary condition for the reality of the spectrum, J. Math. Phys.43 (2002) 205 [math-ph/0107001] [INSPIRE]. I. Duck and E.C.G. Sudarshan, Pauli and the spin-statistics theorem, World Scientific (1997) [INSPIRE]. FeiLGiombiSKlebanovIRTarnopolskyGCritical Sp(N) models in 6 – ϵ dimensions and higher spin dS/CFTJHEP201509076342941110.1007/JHEP09(2015)076[arXiv:1502.07271] [INSPIRE] R.F. Streater and A.S. Wightman, PCT, spin and statistics, and all that, Princeton University Press (1989) [INSPIRE]. S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge University Press (2005). RobinsonDJKapitELeClairALorentz Symmetric Quantum Field Theory for Symplectic FermionsJ. Math. Phys.2009501123012009JMP....50k2301R256718810.1063/1.3248256[arXiv:0903.2399] [INSPIRE] Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641 (2020) A6 [Erratum ibid.652 (2021) C4] [arXiv:1807.06209] [INSPIRE]. AhluwaliaDVMass dimension one fermions: Constructing darknessPhys. Rept.202296712022PhR...967....1A441956610.1016/j.physrep.2022.04.003[arXiv:2205.04754] [INSPIRE] NgGSStromingerAState/Operator Correspondence in Higher-Spin dS/CFTClass. Quant. Grav.2013301040022013CQGra..30j4002N305508510.1088/0264-9381/30/10/104002[arXiv:1204.1057] [INSPIRE] SatoYComments on Entanglement Entropy in the dS/CFT CorrespondencePhys. Rev. D2015912015PhRvD..91h6009S10.1103/PhysRevD.91.086009[arXiv:1501.04903] [INSPIRE] LeClairANeubertMSemi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion modelsJHEP2007100272007JHEP...10..027L235795110.1088/1126-6708/2007/10/027[arXiv:0705.4657] [INSPIRE] D.J. Gross and A. Neveu, Dynamical Symmetry Breaking in Asymptotically Free Field Theories, Phys. Rev. D10 (1974) 3235 [INSPIRE]. NarayanKOn dS4extremal surfaces and entanglement entropy in some ghost CFTsPhys. Rev. D2016942016PhRvD..94d6001N370699810.1103/PhysRevD.94.046001[arXiv:1602.06505] [INSPIRE] S Ryu (23456_CR15) 2023; 130 D Anninos (23456_CR16) 2017; 34 K Narayan (23456_CR20) 2016; 94 23456_CR1 23456_CR5 A LeClair (23456_CR11) 2007; 10 DJ Robinson (23456_CR22) 2009; 50 23456_CR4 23456_CR3 Y Sato (23456_CR19) 2015; 91 23456_CR2 CM Bender (23456_CR7) 2007; 70 23456_CR8 23456_CR6 A Mostafazadeh (23456_CR9) 2010; 7 DV Ahluwalia (23456_CR12) 2022; 967 DV Ahluwalia (23456_CR14) 2023; 987 23456_CR10 GS Ng (23456_CR17) 2013; 30 D Das (23456_CR18) 2013; 01 23456_CR23 L Fei (23456_CR21) 2015; 09 23456_CR13 23456_CR24 |
| References_xml | – reference: S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge University Press (2005). – reference: R.F. Streater and A.S. Wightman, PCT, spin and statistics, and all that, Princeton University Press (1989) [INSPIRE]. – reference: MostafazadehAPseudo-Hermitian Representation of Quantum MechanicsInt. J. Geom. Meth. Mod. Phys.201071191274938510.1142/S0219887810004816[arXiv:0810.5643] [INSPIRE] – reference: P.A.M. Dirac, Quantised singularities in the electromagnetic field, Proc. Roy. Soc. Lond. A133 (1931) 60 [INSPIRE]. – reference: W. Pauli, On Dirac’s New Method of Field Quantization, Rev. Mod. Phys.15 (1943) 175. – reference: Y. Nambu and G. Jona-Lasinio, Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. 1, Phys. Rev.122 (1961) 345 [INSPIRE]. – reference: A. Mostafazadeh, PseudoHermiticity versus PT symmetry. The necessary condition for the reality of the spectrum, J. Math. Phys.43 (2002) 205 [math-ph/0107001] [INSPIRE]. – reference: Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641 (2020) A6 [Erratum ibid.652 (2021) C4] [arXiv:1807.06209] [INSPIRE]. – reference: AhluwaliaDVMass dimension one fermions: Constructing darknessPhys. Rept.202296712022PhR...967....1A441956610.1016/j.physrep.2022.04.003[arXiv:2205.04754] [INSPIRE] – reference: D.V. Ahluwalia and C.-Y. Lee, Spin-half bosons with mass dimension three-half: Evading the spin-statistics theorem, EPL140 (2022) 24001 [Erratum ibid.140 (2022) 69901] [arXiv:2212.09457] [INSPIRE]. – reference: DasDDasSRJevickiAYeQBi-local Construction of Sp(2N)/dS Higher Spin CorrespondenceJHEP2013011072013JHEP...01..107D304550810.1007/JHEP01(2013)107[arXiv:1205.5776] [INSPIRE] – reference: FeiLGiombiSKlebanovIRTarnopolskyGCritical Sp(N) models in 6 – ϵ dimensions and higher spin dS/CFTJHEP201509076342941110.1007/JHEP09(2015)076[arXiv:1502.07271] [INSPIRE] – reference: NgGSStromingerAState/Operator Correspondence in Higher-Spin dS/CFTClass. Quant. Grav.2013301040022013CQGra..30j4002N305508510.1088/0264-9381/30/10/104002[arXiv:1204.1057] [INSPIRE] – reference: AhluwaliaDVda SilvaJMHLeeC-YMass dimension one fields with Wigner degeneracy: A theory of dark matterNucl. Phys. B2023987116092454190010.1016/j.nuclphysb.2023.116092[arXiv:2212.13114] [INSPIRE] – reference: BenderCMMaking sense of non-Hermitian HamiltoniansRept. Prog. Phys.2007709472007RPPh...70..947B233129410.1088/0034-4885/70/6/R03[hep-th/0703096] [INSPIRE] – reference: LeClairANeubertMSemi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion modelsJHEP2007100272007JHEP...10..027L235795110.1088/1126-6708/2007/10/027[arXiv:0705.4657] [INSPIRE] – reference: RyuSYoonJUnitarity of Symplectic Fermions in α Vacua with Negative Central ChargePhys. Rev. Lett.20231302416022023PhRvL.130x1602R460898310.1103/PhysRevLett.130.241602[arXiv:2208.12169] [INSPIRE] – reference: I. Duck and E.C.G. Sudarshan, Pauli and the spin-statistics theorem, World Scientific (1997) [INSPIRE]. – reference: SatoYComments on Entanglement Entropy in the dS/CFT CorrespondencePhys. Rev. D2015912015PhRvD..91h6009S10.1103/PhysRevD.91.086009[arXiv:1501.04903] [INSPIRE] – reference: C.M. Bender and S. 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bstract
The theory of symplectic scalar fermion of LeClair and Neubert is studied. The theory evades the conventional spin-statistics theorem because its... The theory of symplectic scalar fermion of LeClair and Neubert is studied. The theory evades the conventional spin-statistics theorem because its Hamiltonian... Abstract The theory of symplectic scalar fermion of LeClair and Neubert is studied. The theory evades the conventional spin-statistics theorem because its... |
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| SubjectTerms | Classical and Quantum Gravitation Eigenvalues Elementary Particles Evolution Fermions Global Symmetries Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Regular Article - Theoretical Physics Relativity Theory S matrix theory Space-Time Symmetries Spacetime String Theory Symmetry Theorems |
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| Title | Generalized unitary evolution for symplectic scalar fermions |
| URI | https://link.springer.com/article/10.1007/JHEP05(2024)181 https://www.proquest.com/docview/3055264013 https://doaj.org/article/4ea8d7ca31ba4d9e91ac1d221396004e |
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