We study a complex action theory (CAT) whose path runs over not only past but also future. We show that, if we regard a matrix element defined in terms of the future state at time TB and the past state at time TA as an expectation value in the CAT, then we are allowed to have the Heisenberg equation, Ehrenfest's theorem, and the conserved probability current density. In addition, we show that the expectation value at the present time t of a future-included theory for large TB − t and large t − TA corresponds to that of a future-not-included theory with a proper inner product for large t − TA. Hence, the CAT with future explicitly present in the formalism and influencing in principle the past is not excluded phenomenologically, because the effects are argued to be very small in the present era. Furthermore, we explicitly derive the Hamiltonian for the future state via a path integral, and confirm that it is given by the Hermitian conjugate of the Hamiltonian for the past state.We study a complex action theory (CAT) whose path runs over not only past but also future. We show that, if we regard a matrix element defined in terms of the future state at time TB and the past state at time TA as an expectation value in the CAT, then we are allowed to have the Heisenberg equation, Ehrenfest's theorem, and the conserved probability current density. In addition, we show that the expectation value at the present time t of a future-included theory for large TB − t and large t − TA corresponds to that of a future-not-included theory with a proper inner product for large t − TA. Hence, the CAT with future explicitly present in the formalism and influencing in principle the past is not excluded phenomenologically, because the effects are argued to be very small in the present era. Furthermore, we explicitly derive the Hamiltonian for the future state via a path integral, and confirm that it is given by the Hermitian conjugate of the Hamiltonian for the past state.

arXiv:1205.3706Progress of Theoretical and Experimental PhysicsFeb 1, 20135 citations

Future Convergence Theory: A Unified Framework for Delayed Choice, 4D Information Fields, and Quantum Decoherence

悠斗小川

This paper proposes an extended formulation of Future Convergence Theory (FCT) that unifies three major components of modern theoretical physics: quantum delayed-choice experiments, four-dimensional information fields, and quantum decoherence. The theory introduces a novel function, \Lambda(T), representing future certainty, and explores how this function retroactively influences quantum states, information entropy, and energy distribution across spacetime. By incorporating \Lambda(T) into the evolution equations of wavefunctions and entropy, we show that future outcomes can dynamically shape the structure of the past. This framework offers a new interpretation of time and causality, suggesting that the future is not passively received but actively encoded into the informational fabric of the universe. We also discuss experimental possibilities, including quantum entanglement verification, AI-based prediction models, and cosmological observations. The theory aims to expand the foundations of physics by mathematically describing how the future may influence the past through higher-dimensional information dynamics.This paper proposes an extended formulation of Future Convergence Theory (FCT) that unifies three major components of modern theoretical physics: quantum delayed-choice experiments, four-dimensional information fields, and quantum decoherence. The theory introduces a novel function, \Lambda(T), representing future certainty, and explores how this function retroactively influences quantum states, information entropy, and energy distribution across spacetime. By incorporating \Lambda(T) into the evolution equations of wavefunctions and entropy, we show that future outcomes can dynamically shape the structure of the past. This framework offers a new interpretation of time and causality, suggesting that the future is not passively received but actively encoded into the informational fabric of the universe. We also discuss experimental possibilities, including quantum entanglement verification, AI-based prediction models, and cosmological observations. The theory aims to expand the foundations of physics by mathematically describing how the future may influence the past through higher-dimensional information dynamics.

Mar 24, 20253 citations

Effective field theory

CO-PUBLISHED WITH IMPERIAL COLLEGE PRESS eBooksSep 1, 20040 citations

Many body methods and effective field theory

Thomas Schäfer, Chung Wen Kao, Stephen R. Cotanch

arXiv:nucl-th/0504088Nuclear Physics AAug 31, 200560 citations

Reality from maximizing overlap in the future-included real action theory

Keiichi Nagao, Holger Bech Nielsen

In the future-included real action theory whose path runs over not only past but also future, we demonstrate a theorem, which states that the normalized matrix element of a Hermitian operator | $\hat{\mathcal O}$ | defined in terms of the future state at the final time | $T_B$ | and the fixed past state at the initial time | $T_A$ | becomes real for the future state selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. This is a special version of our previously proposed theorem for the future-included complex action theory. We find that though the maximization principle leads to the reality of the normalized matrix element in the future-included real action theory, it does not specify the future and past states so much as in the case of the future-included complex action theory. In addition, we argue that the normalized matrix element seems to be more natural than the usual expectation value. Thus we speculate that the functional integral formalism of quantum theory could be most elegant in the future-included complex action theory.In the future-included real action theory whose path runs over not only past but also future, we demonstrate a theorem, which states that the normalized matrix element of a Hermitian operator |$\hat{\mathcal O}$| defined in terms of the future state at the final time |$T_B$| and the fixed past state at the initial time |$T_A$| becomes real for the future state selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. This is a special version of our previously proposed theorem for the future-included complex action theory. We find that though the maximization principle leads to the reality of the normalized matrix element in the future-included real action theory, it does not specify the future and past states so much as in the case of the future-included complex action theory. In addition, we argue that the normalized matrix element seems to be more natural than the usual expectation value. Thus we speculate that the functional integral formalism of quantum theory could be most elegant in the future-included complex action theory.

arXiv:1705.01585Progress of Theoretical and Experimental PhysicsJun 30, 20171 citation

In the future-included real action theory whose path runs over not only past but also future, we demonstrate a theorem, which states that the normalized matrix element of a Hermitian operator |

\hat{\mathcal O}

| defined in terms of the future state at the final time |

T_B

| and the fixed past state at the initial time |

T_A

| becomes real for the future state selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. This is a special version of our previously proposed theorem for the future-included complex action theory. We find that though the maximization principle leads to the reality of the normalized matrix element in the future-included real action theory, it does not specify the future and past states so much as in the case of the future-included complex action theory. In addition, we argue that the normalized matrix element seems to be more natural than the usual expectation value. Thus we speculate that the functional integral formalism of quantum theory could be most elegant in the future-included complex action theory.