This paper interprets the Feynman path integral, which is a fundamental concept of modern quantum theory, from the perspective of QTIP cosmology. In this interpretation, the conventional Feynman path integral is redefined through the information processing and representation structure of QTIP cosmology, and through this, it is shown that the corresponding path integral can be interpreted as an equation representing the path structure resulting from Tick (T4)-based state transition and the real -domain expression of absolute information proposed in QTIP cosmology.
This paper interprets the Feynman path integral, which is a fundamental concept of modern quantum theory, from the perspective of QTIP cosmology. In this interpretation, the conventional Feynman path integral is redefined through the information processing and representation structure of QTIP cosmology, and through this, it is shown that the corresponding path integral can be interpreted as an equation representing the path structure resulting from Tick (T4)-based state transition and the real -domain expression of absolute information proposed in QTIP cosmology.
This paper aims to examine the EPR paradox and Bell’s theorem, which can be regarded as foundational concepts of modern physics, from the perspective of QTIP cosmology. In modern physics, the EPR paradox, assuming locality and realism, raised questions about the completeness of quantum theory, while Bell’s theorem showed that local hidden-variable theories cannot reproduce the predictions of quantum mechanics. This study attempts an interpretation of these two key proposals based on the premise in QTIP cosmology that absolute information exists in the imaginary domain. Furthermore, it proposes that the imaginary domain in which absolute information exists can be interpreted as Hilbert space, and further presents the possibility that this imaginary-domain absolute-information preservation space may be understood in a realist sense.
This paper proposes a mathematical approach for applying a single Hilbert space (HS) in QTIP Cosmology. Based on the mathematical structure of composite systems in quantum mechanics (QM) and quantum information theory (QIT), it examines the correspondence of superposition, normalization and the Born Rule, entanglement, subsystem measurement statistics, and generalization to N-particle systems. Rather than constructing a new composite Hilbert space through tensor products of independent Hilbert spaces, QTIP Cosmology proposes defining a relational subset HS within a single Hilbert space based on the boundary conditions among QIF_Is. This approach does not exclude the mathematical structures of QM/QIT, but proposes an alternative framework for applying them within a single Hilbert space.
The Feynman path integral does not allow a one real path interpretation, because the quantum amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, all paths happen, is not a useful or informative account. In this paper it is shown that an intermediate parsing of the path integral, into realistic non-interfering possibilities, is always available. Each realistic possibility formally corresponds to numerous particle paths, but is arguably best interpreted as a spacetime-valued field. Notably, one actual field history can always be said to occur, although it will generally not have an extremized action. The most obvious concerns with this approach are addressed, indicating necessary follow-up research. But without obvious showstoppers, it seems plausible that the path integral might be reinterpreted to explain quantum phenomena in terms of Lorentz covariant field histories. Quanta 2016; 5: 1–11.
It has been stated in the physics literature that the probability amplitude for a quantum system after a continuous position measurement can be expressed by the restricted or the weighted Feynman path integral containing information about the result and the resolution of its measurement. In the present paper it is proved that the restricted Feynman path integrals can be defined in a rigorous sense. More specifically, we consider a quantum system consisting of some particles and simultaneously perform a continuous measurement of the positions of all particles in the time interval [0,T]. Then, it is shown rigorously that the restricted Feynman path integral after the measurement can be defined in the L2 space and satisfies the corresponding non-self-adjoint Schroeodinger equation. In addition, our results are generalized to a quantum spin system where a continuous position measurement for all spin components of all particles is simultaneously performed, though the results obtained are inadequate for general use.
The aim of this chapter is to introduce the concept of the Feynman path integral. As well as developing the general construction scheme, particular emphasis is placed on establishing the interconnections between the quantum mechanical path integral, classical Hamiltonian mechanics, and classical statistical mechanics. The practice of path integration is discussed in the context of several pedagogical applications. As well as the canonical examples of a quantum particle in a single and a double potential well, we discuss the generalization of the path integral scheme to tunneling of extended objects (quantum fields), dissipative and thermally assisted quantum tunneling, and the quantum mechanical spin. In this chapter we will temporarily leave the arena of many-body physics and second quantization and, at least superficially, return to single-particle quantum mechanics. By establishing the path integral approach for ordinary quantum mechanics, we will set the stage for the introduction of functional field integral methods for many-body theories explored in the next chapter. We will see that the path integral not only represents a gateway to higher-dimensional functional integral methods but, when viewed from an appropriate perspective, already represents a field theoretical approach in its own right. Exploiting this connection, various techniques and concepts of field theory, namely stationary phase analyses of functional integrals, the Euclidean formulation of field theory, instanton techniques, and the role of topological concepts in field theory, will be motivated and introduced in this chapter.
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates xn. However, the path integral expression cannot be connected to the dynamics of classical mechanics, even though, superficially, there is some similarity between them. Further, the field theory path integral in terms of many dimensional integrations over fields does not correspond to the field quantization. We clarify the essential difference between Feynman's original formulation of path integral in QED and the modern version of the path integral method prevailing in lattice field theory calculations, and show that the former can make a correct second quantization while the latter cannot quantize fields at all and its physical meaning is unknown.