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P,T,PT, and CPT invariance of Hermitian Hamiltonians

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Zafar Ahmed

Quantum Physics · Submitted 11 Feb 2003

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We propose generalized definitions of time-reversal operator (T) and orthonormality such that all Hermitian Hamiltonians are P, T, PT, and CPT invariant.

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arXiv IDquant-ph/0302084 (version 2)
Pith IDLJ6NX4OF, Pith's permanent record of this paper and its review
CitationZafar Ahmed. "P,T,PT, and CPT invariance of Hermitian Hamiltonians." arXiv:quant-ph/0302084 (2003). https://pith.science/paper/LJ6NX4OF
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,814 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.80 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Currently, it has been claimed that certain Hermitian Hamiltonians have parity (P) and they are PT-invariant. We propose generalized definitions of time-reversal operator (T) and orthonormality such that all Hermitian Hamiltonians are P, T, PT, and CPT invariant. The PT-norm and CPT-norm are indefinite and definite respectively. The energy-eigenstates are either E-type (e.g., even) or O-type (e.g., odd). C mimics the charge-conjugation symmetry which is recently found to exist for a non-Hermitian Hamiltonian. For a Hermitian Hamiltonian it coincides with P.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Currently, it has been claimed that certain Hermitian Hamiltonians have parity (P) and they are PT-invariant. background 0.99 0.04 0.04 asserted 0.93
s1 We propose generalized definitions of time-reversal operator (T) and orthonormality such that all Hermitian Hamiltonians are P, T, PT, and CPT invariant. contribution 0.99 0.89 0.80 asserted 0.84
s2 The PT-norm and CPT-norm are indefinite and definite respectively. result 0.98 0.71 0.10 asserted 1.00
s3 The energy-eigenstates are either E-type (e.g., even) or O-type (e.g., odd). result 0.87 0.73 0.06 asserted 1.00
s4 C mimics the charge-conjugation symmetry which is recently found to exist for a non-Hermitian Hamiltonian. background 0.47 0.15 0.04 asserted 0.98
s5 For a Hermitian Hamiltonian it coincides with P. result 0.88 0.51 0.07 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.85 · evidence from proof or derivation 0.60.

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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Currently, it has been claimed that certain Hermitian Hamiltonians have parity (P) and they are PT-invariant. We propose generalized definitions of time-reversal operator (T) and orthonormality such that all Hermitian Hamiltonians are P, T, PT, and CPT invariant. The PT-norm and CPT-norm are indefinite and definite respectively. The energy-eigenstates are either E-type (e.g., even) or O-type (e.g., odd). C mimics the charge-conjugation symmetry which is recently found to exist for a non-Hermitian Hamiltonian. For a Hermitian Hamiltonian it coincides with P.

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