Multiparticle Field Research Articles

Laplace’s method for elastic scattering diagrams within multiparticle fields model

We apply the multiparticle fields model to calculate the differential cross section $d\ensuremath{\sigma}/dt$ of elastic proton-proton scattering. This problem includes the calculation of multidimensional integrals arising from the loop Feynman diagrams. We demonstrated how these integrals can be reduced with Laplace's method to one- and two-dimensional integrals which can be calculated numerically. The obtained result qualitatively describes the minimum in differential cross section dependency $d\ensuremath{\sigma}/dt(t)$.

Manifest colour-kinematics duality and double-copy in the string-based formalism

The relation for the gravity polarisation tensor as the tensor product of two gluon polarisation vectors has been well-known for a long time, but a version of this relation for multi-particle fields is presently still not known. Here we show that in order for this to happen we first have to ensure that the multi-particle polarisations satisfy colour-kinematics duality. In previous work it has been show that this arises naturally from the Bern-Kosower formalism for one-loop gluon amplitudes, and here we show that the tensor product for multi-particle fields arises naturally in the Bern-Dunbar-Shimada formalism for one-loop gravity amplitudes. This allows us to formulate a new prescription for double-copy gravity Berends-Giele currents, and to obtain both the colour-dressed Yang-Mills Berends-Giele currents in the Bern-Carrasco-Johansson gauge and the gravitational Berends-Giele currents explicitly. An attractive feature of our formalism is that it never becomes necessary to determine gauge transformation terms. Our double-copy prescription can also be applied to other cases, and to make this point we derive the double-copy perturbiners for α′-deformed gravity and the bi-adjoint scalar model.

Color-kinematics duality from the Bern-Kosower formalism

Berends-Giele currents are fundamental building blocks for on-shell amplitudes in non-abelian gauge theory. We present a novel procedure to construct them using the Bern-Kosower formalism for one-loop gluon amplitudes. Applying the pinch procedure of that formalism to a suitable special case the currents are naturally obtained in terms of multi-particle fields and obeying colour-kinematics duality. As a feedback to the Bern-Kosower formalism we outline how the multi-particle polarisations and field-strength tensors can be used to significantly streamline the pinch procedure.

κ -Poincaré comodules, braided tensor products, and noncommutative quantum field theory

We discuss the obstruction to the construction of a multiparticle field theory on a $\kappa$-Minkowski noncommutative spacetime: the existence of multilocal functions which respect the deformed symmetries of the problem. This construction is only possible for a light-like version of the commutation relations, if one requires invariance of the tensor product algebra under the coaction of the $\kappa$-Poincar\'e group. This necessitates a braided tensor product. We study the representations of this product, and prove that $\kappa$-Poincar\'e-invariant N-point functions belong to an Abelian subalgebra, and are therefore commutative. We use this construction to define the 2-point Whightman and Pauli--Jordan functions, which turn out to be identical to the undeformed ones. We finally outline how to construct a free scalar $\kappa$-Poincar\'e-invariant quantum field theory, and identify some open problems.

One-loop correlators and BCJ numerators from forward limits

We present new formulas for one-loop ambitwistor-string correlators for gauge theories in any even dimension with arbitrary combinations of gauge bosons, fermions and scalars running in the loop. Our results are driven by new all-multiplicity expressions for tree-level two-fermion correlators in the RNS formalism that closely resemble the purely bosonic ones. After taking forward limits of tree-level correlators with an additional pair of fermions/bosons, one-loop correlators become combinations of Lorentz traces in vector and spinor representations. Identities between these two types of traces manifest all supersymmetry cancellations and the power counting of loop momentum. We also obtain parity-odd contributions from forward limits with chiral fermions. One-loop numerators satisfying the Bern-Carrasco-Johansson (BCJ) duality for diagrams with linearized propagators can be extracted from such correlators using the well-established tree-level techniques in Yang-Mills theory coupled to biadjoint scalars. Finally, we obtain streamlined expressions for BCJ numerators up to seven points using multiparticle fields.

Multiparticle Fields on the Subset of Simultaneity

We propose a model describing the scattering of hadrons as bound states of their constituent quarks. We build the dynamic equations for the multiparticle fields on the subset of simultaneity, using the Lagrange method, similarly to the case of “usual” single-particle fields. We then consider the gauge fields restoring the local internal symmetry on the subset of simultaneity. Since the multiparticle fields, which describe mesons as bound states of a quark and an antiquark, are two-index tensors relative to the local gauge group, it is possible to consider a model with two different gauge fields, each one associated with its own index. Such fields would be transformed by the same laws during a local gauge transformation and satisfy the same dynamic equations, but with different boundary conditions. The dynamic equations for the multiparticle gauge fields describe such phenomena as the confinement and the asymptotic freedom of colored objects under certain boundary conditions and the spontaneous symmetry breaking under another ones. With these dynamic equations, we are able to describe the quark confinement in hadrons within a single model and their interaction during the hadron scattering through the exchange of the bound states of gluons – the glueballs.

Multi-particle fields and Higgs mechanism

Multi-particle fields and Higgs mechanism

Scattering amplitudes in open superstring theory

AbstractThis review is concerned with scattering amplitudes in open superstring theories. In particular, we introduce two different formalisms to compute tree level amplitudes – the Ramond Neveu Schwarz‐ (RNS‐) and the Pure Spinor (PS‐) formalism. The RNS approach proves to be flexible in describing compactifications from ten to four flat spacetime dimensions. We solve the technical problems due to the underlying interacting conformal field theory on the worldsheet. This is exploited to extract phenomenologically relevant scattering amplitudes of gluons and quarks as well as production‐ and decay rates of massive vibration modes which have already been identified as virtual exchange particles at the massless level. In case of a TeV string scale, string specific signatures in parton collisions might be observed at the LHC experiment in the near future and constitute the first experimental evidence for string theory. These statements apply to a wide class of string vacua and therefore bypass the so‐called landscape problem of string theory. The PS formalism allows for a manifestly supersymmetric treatment of scattering amplitudes in ten spacetime dimensions with sixteen supercharges. We introduce a family of superfields which arises in tree amplitudes of massless open string states and can be naturally identified with diagrams made of cubic vertices. We firstly achieve a compact superspace representation of multiparticle field theory amplitudes and moreover express the complete n point superstring amplitude as a minimal linear combination of partial field theory amplitudes and hypergeometric functions. The latter carry the stringy effects and are analyzed from different perspectives.

Entanglement Test on a Microscopic-Macroscopic System

A macrostate consisting of N approximately 3.5x10{4} photons in a quantum superposition and entangled with a far apart single-photon state (microstate) is generated. Precisely, an entangled photon pair is created by a nonlinear optical process; then one photon of the pair is injected into an optical parametric amplifier operating for any input polarization state, i.e., into a phase-covariant cloning machine. Such transformation establishes a connection between the single photon and the multiparticle fields. We then demonstrate the nonseparability of the bipartite system by adopting a local filtering technique within a positive operator valued measurement.

Asymptotische Mehrteilchen-Feldoperatoren für phänomenologische Potentiale

In W. Sandhas’ field theoretical formulation1 of the nonrelativistic multichannel scattering theory the existence of asymptotic multiparticle field operators is discussed for phenomenological potentials. For potentials with momentum-dependent terms it is necessary to treat the convergence of time-dependent field operators on a special subset, — dense in the Hilbert space of states; concerning the position-dependency of tensor- and angular momentum-forces it is necessary to make use of a sharpened asymptotic condition.