The Cheshire Cat Principle from Holography

The Cheshire cat principle states that hadronic observables at low energy do not distinguish between hard (quark) or soft (meson) constituents. As a result, the delineation between hard/soft (bag radius) is like the Cheshire cat smile in Alice in wonderland. This principle reemerges from current holographic descriptions of chiral baryons whereby the smile appears in the holographic direction. We illustrate this point for the baryonic form factor.Comment: 11 pages, 2 figure

Formalism of a harmonic oscillator in the future-included complex action theory

In a special representation of complex action theory that we call ``future-included'', we study a harmonic oscillator model defined with a non-normal Hamiltonian $\hat{H}$, in which a mass $m$ and an angular frequency $\omega$ are taken to be complex numbers. In order for the model to be sensible some restrictions on $m$ and $\omega$ are required. We draw a phase diagram in the plane of the arguments of $m$ and $\omega$, according to which the model is classified into several types. In addition, we formulate two pairs of annihilation and creation operators, two series of eigenstates of the Hamiltonians $\hat{H}$ and $\hat{H}^\dag$, and coherent states. They are normalized in a modified inner product $I_Q$, with respect to which the Hamiltonian $\hat{H}$ becomes normal. Furthermore, applying to the model the maximization principle that we previously proposed, we obtain an effective theory described by a Hamiltonian that is $Q$-Hermitian, i.e. Hermitian with respect to the modified inner product $I_Q$. The generic solution to the model is found to be the ``ground'' state. Finally we discuss what the solution implies.Comment: Latex 42 pages, 3 figures, typos corrected, presentation improved, the final version to appear in Prog.Theor.Exp.Phy

Complex action suggests future-included theory

In quantum theory its action is usually taken to be real, but we can consider another theory whose action is complex. In addition, in the Feynman path integral, the time integration is usually performed over the period between the initial time $T_A$ and some specific time, say, the present time $t$. Besides such a future-not-included theory, we can consider the future-included theory, in which not only the past state $| A(T_A) \rangle$ at the initial time $T_A$ but also the future state $| B(T_B) \rangle$ at the final time $T_B$ is given at first, and the time integration is performed over the whole period from the past to the future. Thus quantum theory can be classified into four types, according to whether its action is real or not, and whether the future is included or not. We argue that, if a theory is described with a complex action, then such a theory is suggested to be the future-included theory, rather than the future-not-included theory. Otherwise persons living at different times would see different histories of the universe.Comment: Latex 12 pages, 3 figures, typo corrected, presentation improved, the final version to appear in Prog.Theor.Exp.Phy

Automatic Hermiticity

We study a diagonalizable Hamiltonian that is not at first hermitian. Requirement that a measurement shall not change one Hamiltonian eigenstate into another one with a different eigenvalue imposes that an inner product must be defined so as to make the Hamiltonian normal with regard to it. After a long time development with the non-hermitian Hamiltonian, only a subspace of possible states will effectively survive. On this subspace the effect of the anti-hermitian part of the Hamiltonian is suppressed, and the Hamiltonian becomes hermitian. Thus hermiticity emerges automatically, and we have no reason to maintain that at the fundamental level the Hamiltonian should be hermitian. If the Hamiltonian is given in a local form, a conserved probability current density can be constructed with two kinds of wave functions. We also point out a possible misestimation of a past state by extrapolating back in time with the hermitian Hamiltonian. It is a seeming past state, not a true one.Comment: 8 pages, references added, typos etc. corrected, the final version to appear in Prog.Theor.Phy

Seeking a Game in which the standard model Group shall Win

It is attempted to construct a group-dependent quantity that could be used to single out the Standard Model group S(U(2) x U(3)) as being the "winner" by this quantity being the biggest possible for just the Standard Model group. The suggested quantity is first of all based on the inverse quadratic Cassimir for the fundamental or better smallest faithful representation in a notation in which the adjoint representation quadratic Cassimir is normalized to unity. Then a further correction is added to help the wanted Standard Model group to win and the rule comes even to involve the Abelian group U(1) to be multiplied into the group to get this correction be allowed. The scheme is suggestively explained to have some physical interpretation(s). By some appropriate proceedure for extending the group dependent quantity to groups that are not simple we find a way to make the Standard Model Group the absolute "winner". Thus we provide an indication for what could be the reason for the Standard Model Group having been chosen to be the realized one by Nature.Comment: already publiched in 2011 in Bled Conference proceedings "What comes beyond the Stadard Models