General properties of eigenvectors and eigenvalues for an effective Hamiltonian governing time evolution in a two state subspace of the state space of the total system under consideration are discussed. The Lee, Oehme and Yang (LOY) theory of time evolution in such a subspace and CP-- and CPT--symmetry properties of the LOY effective Hamiltonian are considered. The CPT transformation properties of the exact effective Hamiltonian for two state subspace are discussed also. Using the Khalfin Theorem we show that contrary to the properties of the LOY theory, the diagonal matrix elements of the exact effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for $t > t_{0}$ ( $t_{0}$ is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. Using the more accurate approximation than the LOY one we show that the interpretation of the tests measuring the difference between the $K_{0}$ mass and the ${\\bar K}_{0}$ mass as the CPT--symmetry test is wrong.General properties of eigenvectors and eigenvalues for an effective Hamiltonian governing time evolution in a two state subspace of the state space of the total system under consideration are discussed. The Lee, Oehme and Yang (LOY) theory of time evolution in such a subspace and CP-- and CPT--symmetry properties of the LOY effective Hamiltonian are considered. The CPT transformation properties of the exact effective Hamiltonian for two state subspace are discussed also. Using the Khalfin Theorem we show that contrary to the properties of the LOY theory, the diagonal matrix elements of the exact effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for $t > t_{0}$ ($t_{0}$ is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. Using the more accurate approximation than the LOY one we show that the interpretation of the tests measuring the difference between the $K_{0}$ mass and the ${\\bar K}_{0}$ mass as the CPT--symmetry test is wrong.

Jan 1, 20052 citations

Dynamical symmetries in quantum theory

Evelyn Aronson, I.A. Malkin, Vladimir I. Man’ko

Jul 1, 19742 citations

Subsystem of neutral mesons beyond the Lee-Oehme-Yang approximation

K. Urbanowski

General properties of eigenvectors and eigenvalues for an effective Hamiltonian governing time evolution in a two state subspace of the state space of the total system under consideration are discussed. The Lee, Oehme and Yang (LOY) theory of time evolution in such a subspace and CP-- and CPT--symmetry properties of the LOY effective Hamiltonian are considered. The CPT transformation properties of the exact effective Hamiltonian for two state subspace are discussed also. Using the Khalfin Theorem we show that contrary to the properties of the LOY theory, the diagonal matrix elements of the exact effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for $t > t_{0}$ ( $t_{0}$ is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. Using the more accurate approximation than the LOY one we show that the interpretation of the tests measuring the difference between the $K_{0}$ mass and the ${\bar K}_{0}$ mass as the CPT--symmetry test is wrong.General properties of eigenvectors and eigenvalues for an effective Hamiltonian governing time evolution in a two state subspace of the state space of the total system under consideration are discussed. The Lee, Oehme and Yang (LOY) theory of time evolution in such a subspace and CP-- and CPT--symmetry properties of the LOY effective Hamiltonian are considered. The CPT transformation properties of the exact effective Hamiltonian for two state subspace are discussed also. Using the Khalfin Theorem we show that contrary to the properties of the LOY theory, the diagonal matrix elements of the exact effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for $t > t_{0}$ ($t_{0}$ is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. Using the more accurate approximation than the LOY one we show that the interpretation of the tests measuring the difference between the $K_{0}$ mass and the ${\bar K}_{0}$ mass as the CPT--symmetry test is wrong.

arXiv:hep-ph/0405070May 8, 20040 citations

Dynamical groups and generalized symmetries in quantum theory : with applications in atomic and particle physics

Asım Orhan Barut

Jan 1, 197233 citations

Symmetries in discrete-time quantum field theory

George Jaroszkiewicz

Physics of Atomic NucleiNov 1, 19980 citations

CPT and effective Hamiltonians for neutral kaon and similar complexes*

K. Urbanowski

This paper begins with a discussion of the general form and general CP-and CPT-transformation properties of the Lee-Oehme--Yang (LOY) effective Hamiltonian for the neutral kaon complex.Next, the properties of the exact effective Hamiltonian determined by the properties of the exact transition amplitudes for this complex are discussed.Using the Khalfin Theorem we show that contrary to the standard result of the LOY theory, the diagonal matrix elements of the effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for t > t 0 (t 0 is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant.The unusual consequence of this result is that, contrary to the properties of stable particles, the masses of the unstable particle "1" and its antiparticle "2" need not be equal for t o t 0 in the case of preserved CPT and violated CP symmetries.We also show that there exists an approximation which is more accurate than the LOY, and which leads to an effective Hamiltonian whose diagonal matrix elements posses properties consistent with the conclusions for the exact effective Hamiltonian described above.This paper begins with a discussion of the general form and general CP-and CPT-transformation properties of the Lee-Oehme--Yang (LOY) effective Hamiltonian for the neutral kaon complex.Next, the properties of the exact effective Hamiltonian determined by the properties of the exact transition amplitudes for this complex are discussed.Using the Khalfin Theorem we show that contrary to the standard result of the LOY theory, the diagonal matrix elements of the effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for t > t 0 (t 0 is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant.The unusual consequence of this result is that, contrary to the properties of stable particles, the masses of the unstable particle "1" and its antiparticle "2" need not be equal for t o t 0 in the case of preserved CPT and violated CP symmetries.We also show that there exists an approximation which is more accurate than the LOY, and which leads to an effective Hamiltonian whose diagonal matrix elements posses properties consistent with the conclusions for the exact effective Hamiltonian described above.

Computational Methods in Science and TechnologyJan 30, 20200 citations

t > t_{0}

(

t_{0}

is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. Using the more accurate approximation than the LOY one we show that the interpretation of the tests measuring the difference between the

K_{0}

mass and the

{\\bar K}_{0}

mass as the CPT--symmetry test is wrong.

t > t_{0}

(

t_{0}

K_{0}

mass and the

{\bar K}_{0}

mass as the CPT--symmetry test is wrong.