Related papers: Transitioning from equal-time to light-front quant…
There is a discrepancy between light-front and equal-time values for the critical coupling of two-dimensional $\phi^4$ theory. A proposed resolution is to take into account the difference between mass renormalizations in the two…
We develop a method by which vacuum transitions may be included in light-front calculations. This allows tadpole contributions which are important for symmetry-breaking effects and yet are missing from standard light-front calculations.…
We compare light-front quantization and instant-time quantization both at the level of operators and at the level of their Feynman diagram matrix elements. At the level of operators light-front quantization and instant-time quantization…
It is often stated that the vacuum is trivial when light-front (null-plane) quantization is applied to a quantum field theory, in contrast to the situation with equal-time quantization. In fact, it is has long been known that the statement…
The renormalization of the two dimensional light-front quantized $\phi^{4}$ theory is discussed. The mass renormalization condition and the renormalized constraint equation are shown to contain all the information to describe the phase…
We revisit the problem of quantizing field theories on noncommutative Moyal spacetime with \emph{light-like} noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front…
We discuss the vacuum structure of $\phi^4$-theory in 1+1 dimensions quantised on the light-front $x^+ =0$. To this end, one has to solve a non-linear, operator-valued constraint equation. It expresses that mode of the field operator having…
The field theory quantized on the {\it light-front} is compared with the conventional equal-time quantized theory. The arguments based on the {\it microcausality} principle imply that the light-front field theory may become nonlocal with…
We use the light front ``machinery'' to study the behavior of a relativistic free particle and obtain the quantum commutation relations from the classical Poisson brackets. We argue that their usual projection onto the light-front…
Modes with zero longitudinal light-front momentum (zero modes) do have roles to play in the analysis of light-front field theories. These range from improvements in convergence for numerical calculations to implications for the light-front…
The light-front Hamiltonian formulation for the scalar field theory contains a new ingredient in the form of a constraint equation. Renormalization of the two dimensional $\phi^{4}$ theory, described in the continuum, is discussed. The mass…
Canonical quantization of quantum field theory models is inherently related to the Lorentz invariant partition of classical fields into the positive and the negative frequency parts $u(x) = u^+(x) + u^-(x),$ performed with the help of…
A genuine continuum treatment of the massive \phi^4_{1+1}-theory in light-cone quantization is proposed. Fields are treated as operator valued distributions thereby leading to a mathematically well defined handling of ultraviolet and light…
We reproduce Chang's duality condition in a regularized $\phi^4_{1+1}$ theory quantized on a light front. The regularization involves higher derivatives in the Lagrangian, renders the model finite in the ultraviolet, and does not require…
The Casimir force between conducting plates at rest in an inertial frame is usually computed in equal-time quantization, the natural choice for the given boundary conditions. We show that the well-known result obtained in this way can also…
As a first numerical application of the light-front coupled-cluster (LFCC) method, we consider the odd-parity massive eigenstate of $\phi_{1+1}^4$ theory. The eigenstate is built as a Fock-state expansion in light-front quantization, where…
These lecture notes review the foundations and some applications of light-cone quantization. First I explain how to choose a time in special relativity. Inclusion of Poincare invariance naturally leads to Dirac's forms of relativistic…
Within a scheme of light front quantization of $\phi^4_{1+1}$, it is demonstrated that dynamics of zero modes implies phase transition, and that the critical value of the coupling coincides with the one of the equal time quantization.
Commutation or anticommutation relations quantized at equal instant time and commutation or anticommutation relations quantized at equal light-front time cannot be transformed into each other. While they would thus appear to describe…
In the first part of my lectures, I will use the example of deep-inelastic scattering to explain why light-front coordinates play a distinguished role in many high energy scattering experiments. After a brief introduction into the concept…