Understanding quantum entanglement by thermo field dynamics

We propose a new method to understand quantum entanglement using the thermo field dynamics (TFD) described by a double Hilbert space. The entanglement states show a quantum-mechanically complicated behavior. Our new method using TFD makes it easy to understand the entanglement states, because the states in the tilde space in TFD play a role of tracer of the initial states. For our new treatment, we define an extended density matrix on the double Hilbert space. From this study, we make a general formulation of this extended density matrix and examine some simple cases using this formulation. Consequently, we have found that we can distinguish intrinsic quantum entanglement from the thermal fluctuations included in the definition of the ordinary quantum entanglement at finite temperatures. Through the above examination, our method using TFD can be applied not only to equilibrium states but also to non-equilibrium states. This is shown using some simple finite systems in the present paper.     

Non-commutative geometry and the closed bosonic string

We propose an action for an interacting closed bosonic string. Our formalism relies heavily on ideas discussed by Witten for the open bosonic string. We also obtain the gauge fixed quantum action for the fully interacting open bosonic string.     

Covariant open string field theory on multiple Dp-branes

We study covariant open bosonic string field theories on multiple Dp-branes by using the deformed cubic string field theory, which is equivalent to string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple Dp-branes, we obtain the field theoretical effective action in the zero-slope limit. On multiple D0-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind(BFSS) matrix model. We also discuss the relation between open string field theory on multiple D-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya(IKKT) matrix model.The covariant open string field theory on multiple Dp-branes could be useful to study the non-perturbative properties of quantum field theories in(p+1)-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using covariant string field theory.     

The Born-Infeld action from conformal invariance of the open superstring

We show that the one-loop approximation to sigma-model perturbation theory for the open-superstring leads to the low-energy effective action of Born-Infeld for the gauge field coupled to the ends of the string. Thus the bosonic part of the low-energy open superstring effective action is just that of the open bosinic string. We also that these results are exact to all loop orders of sigma-model perturbation theory.     

Symmetries of the interacting gauge-covariant bosonic string

We derive in detail the local gauge transformations and interaction lagrangian of the second-quantized bosonic string. We verify at lowest non-trivial order in the coupling constant the gauge invariance of the interacting action, and the closure of the field transformations. This gives the structure constants of the corresponding local gauge group. This group has its generators labelled by all the string states of the theory. We show that the fermionic part of the interaction is just the overlap condition for the ghost coordinates of the three strings, multiplied by an appropriate extra ghost at the point common to the three strings. Our treatment is based on an extensive use of Goto-Naka-type overlap equations. It avoids the use of ill-defined infinite matrices or series, and can be straightforwardly extended to other string theories. We explicitly derive the conformal transformation relating the gauge-covariant three-point function to the old Caneschi-Schwimmer-Veneziano vertex. We also deal with the closed bosonic string.     

D-branes on Calabi-Yau spaces and their mirrors

We study the boundary states of D-branes wrapped around supersymmetric cycles in a general Calabi-Yau manifold. In particular, we show how the geometric data on the cycles are encoded in the boundary states. As an application, we analyze how the mirror symmetry transforms D-branes, and we verify that it is consistent with the conjectured periodicity and the monodromy of the Ramond-Ramond field configuration on a Calabi-Yau manifold. This also enables us to study open string worldsheet instanton corrections and relate them to closed string instanton counting. The cases when the mirror symmetry is realized as T-duality are also discussed.     

Thermal Schrödinger Equation: Efficient Tool for Simulation of Many‐Body Quantum Dynamics at Finite Temperature

We develop a wave‐function‐based method for the simulation of quantum dynamics of systems with many degrees of freedom at finite temperature. The method is inspired by the ideas of Thermo Field Dynamics (TFD). As TFD, our method is based on the doubling of the system's degrees of freedom and thermal Bogoliubov transformation. As distinct from TFD, our method implements the doubling of thermalized degrees of freedom only, and relies upon the explicitly constructed generalized thermal Bogoliubov transformation, which is not restricted to fermionic and bosonic degrees of freedom. This renders the present approach computationally efficient and applicable to a large variety of systems.     

A covariant open bosonic string field theory including the endpoint and middlepoint interaction

Extending the usual endpoint and midpoint interactions, we introduce numerous kinds of interactions, labelled by a parameter λ and obtain a non-commutative and associative string field algebra by adding up all interactions. With this algebra we develop a covariant open bosonic string field theory, which reduces to Witten's open bosonic string field theory under a special string length choice.     

Fock space formulation of gauge invariant interacting field theories of open and closed strings

We derive the conditions that must be satisfied by three string vertex operators, in order to have a gauge invariant Chern-Simons type action as proposed by Witten for the open bosonic string, in a Fock space formulation. Given a vertex which satisfies these conditions for the open string, we show how to construct an invariant action for the closed string.     

具有有限温度的热克尔态

利用热场动力学方法，提出了具有有限温度的热克尔态，研究了这些态的量子统计性质及其与温度的关系，讨论了这些态中场振幅的涨落与压缩性质．对于热化的场，还提出了热压缩的定义，并对热克尔态，讨论了温度对热压缩的影响     

String lessons for higher-spin interactions

String Theory includes a plethora of higher-spin excitations, which clearly lie behind its most spectacular properties, but whose detailed behavior is largely unknown. Conversely, string interactions contain much useful information on higher-spin couplings, which can be very valuable in current attempts to characterize their systematics. We present a simplified form for the three-point (and four-point) amplitudes of the symmetric tensors belonging to the first Regge trajectory of the open bosonic string and relate them to local couplings and currents. These include the cases first discussed, from a field theory perspective, by Berends, Burgers and van Dam, and generalize their results in a suggestive fashion along lines recently explored by Boulanger, Metsaev and others. We also comment on the recovery of gauge symmetry in the low-tension limit, on the current-exchange amplitudes that can be built from these couplings and on the extension to mixed-symmetry states.     

A Path Integral Approach¶to the Kontsevich Quantization Formula

We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory. Its Batalin–Vilkovisky quantization yields a superconformal field theory. The associativity of the star product, and more generally the formality conjecture can then be understood by field theory methods. As an application, we compute the center of the deformed algebra in terms of the center of the Poisson algebra. Received: 10 March 1999 / Accepted: 30 January 2000     

Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems

In this paper, we consider the thermal bath Lindblad master equation to describe the quantum nonunitary dynamics of quantum states in a multi-mode bosonic system. For the two-mode bosonic system interacting with an environment, we analyse how both the coupling between the modes and the coupling with the environment characterised by the frequency and the relaxation rate vectors affect dynamics of the entanglement. We discuss how the revivals of entanglement can be induced by the dynamic coupling between the different modes. For the system, initially prepared in a two-mode squeezed state, we find the logarithmic negativity as defined by the magnitude and orientation of the frequency and the relaxation rate vectors. We show that, in the regime of finite-time disentanglement, reorientation of the relaxation rate vector may significantly increase the time of disentanglement.     

Conformal gravity and the bosonic string

We show that the Callan et al. effective equations of motion for the bosonic closed string in a non-trivial background may not be derived only from the bosonic part of theN=1 supergravity action of Manton and Chapline, but also from just a general conformally invariant theory of gravity. In our scheme the invariance under gauge transformations of the antisymmetric tensor field turns out to be a consequence of the metricity condition.     

One loop partition functions in a compactified open bosonic string theory

We calculate the one loop partition functions of a toroidally compactified open bosonic string (fromD=26 toD=10) in the path integral formalism. By a certain combination of the compactified sectors it is shown that the partition functions of a compactified open bosonic string vanish in both annulus and Möbius strip topologies as in the open superstring case. We also discuss the consistency requirement for the equivalence between the compactified open bosonic string and the open superstring with the gauge groups (SO(8192) andSO(32), respectively.     

The Pomeron in Closed Bosonic String Theory

We review the features of the pomeron in the S-matrix theory and in quantum field theory. We extend those general properties to the pomeron of closed bosonic string theory in a Minkowskian background. We compute the couplings of the pomeron to the first few mass levels of closed bosonic string states in flat space. We recognize the deviation from the linearity of the Regge trajectories in a five dimensional anti De Sitter background.     

Dual Peierls brackets for strings

A new type of Peierls bracket which provides an additional representation of the Virasoro algebra, and which may be of relevance for a manifestly dual string field theory is constructed for the closed and open bosonic strings.     

High-energy zero-norm states and symmetries of string theory

High-energy limit of zero-norm states in the old covariant first quantized spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive infinitely many linear relations among the leading high-energy, fixed-angle behavior of four-point functions of different string states. As a result, ratios among all high-energy scattering amplitudes of four arbitrary string states can be calculated algebraically and the leading order amplitudes can be expressed in terms of that of four tachyons as conjectured by Gross in 1988. A dual calculation can also be performed and equivalent results are obtained by taking the high-energy limit of Virasoro constraints. Finally, we compute all high-energy scattering amplitudes of three tachyons and one massive state at the leading order by saddle-point approximation to verify our results.     

Dynamical rearrangement of the thermal vacuum in thermo field dynamics

The dynamical rearrangement of the thermal vacuum is investigated within the framework of the thermo field dynamics (TFD). For the cases where the initial state and the final state of a system have different symmetries, models of the boson transformation and the superconductor are dealt with to show how to use the axioms of TFD. It is shown that TFD can treat the time evolution of the symmetry breaking systematically. Although the investigation is done within the lowest order treatment in this paper, the dynamical rearrangement of the thermal vacuum can be observed because of the presence of the dissipative part in the time evolution generator of TFD.