Interaction of a Magnet and a Point Charge: Unrecognized Internal Electromagnetic Momentum

Whereas nonrelativistic mechanics always connects the total momentum of a system to the motion of the center of mass, relativistic systems, such as interacting electromagnetic charges, can have internal linear momentum in the absence of motion of the center of energy of the system. This internal linear momentum of the system is related to the controversial concept of "hidden momentum." We suggest that the term "hidden momentum" be abandoned. Here we use the relativistic conservation law for the center of energy to give an unambiguous definition of the "internal momentum of a system," and then we exhibit this internal momentum for the system of a magnet (modeled as a circular ring of moving charges) and a distant static point charge. The calculations provide clear illustrations of this system for three cases: a) the moving charges of the magnet are assumed to continue in their unperturbed motion, b) the moving charges of the magnet are free to accelerate but have no mutual interactions, and c) the moving charges of the magnet are free to accelerate and also interact with each other. It is noted that when the current-carrying charges of the magnet are allowed to interact, the magnet itself will contain internal electromagnetic linear momentum, something which has not been presented clearly in the research and teaching literature.Comment: 23 pages. This manuscript is related to arXiv:1408.3741, but has been thoroughly revised with a different focu

Unexpected Features of Supersymmetry with Central Charges

It is shown that N=2 supersymmetric theories with central charges present some hidden quartic symmetry. This enables us to construct representations of the quartic structure induced by superalgebra representations.Comment: 14 pages, more details have been given, to appear in J. Phys.

Discovering hidden sectors with mono-photon Z' searches

In many theories of physics beyond the Standard Model, from extra dimensions to Hidden Valleys and models of dark matter, Z' bosons mediate between Standard Model particles and hidden sector states. We study the feasibility of observing such hidden states through an invisibly decaying Z' at the LHC. We focus on the process pp -> \gamma Z' -> \gamma X X*, where X is any neutral, (quasi-) stable particle, whether a Standard Model (SM) neutrino or a new state. This complements a previous study using pp -> Z Z' -> l+ l- X X*. Only the Z' mass and two effective charges are needed to describe this process. If the Z' decays invisibly only to Standard Model neutrinos, then these charges are predicted by observation of the Z' through the Drell-Yan process, allowing discrimination between Z' decays to SM neutrinos and invisible decays to new states. We carefully discuss all backgrounds and systematic errors that affect this search. We find that hidden sector decays of a 1 TeV Z' can be observed at 5 sigma significance with 50 fb^{-1} at the LHC. Observation of a 1.5 TeV state requires super-LHC statistics of 1 ab^{-1}. Control of the systematic errors, in particular the parton distribution function uncertainty of the dominant Z \gamma background, is crucial to maximize the LHC searchComment: 13 pages, 4 figure

Matching Higher Conserved Charges for Strings and Spins

We demonstrate that the recently found agreement between one-loop scaling dimensions of large dimension operators in N=4 gauge theory and energies of spinning strings on AdS_5 x S^5 extends to the eigenvalues of an infinite number of hidden higher commuting charges. This dynamical agreement is of a mathematically highly intricate and non-trivial nature. In particular, on the gauge side the generating function for the commuting charges is obtained by integrable quantum spin chain techniques from the thermodynamic density distribution function of Bethe roots. On the string side the generating function, containing information to arbitrary loop order, is constructed by solving exactly the Backlund equations of the integrable classical string sigma model. Our finding should be an important step towards matching the integrable structures on the string and gauge side of the AdS/CFT correspondence.Comment: Latex, 33 pages, v2: new section added (completing the analytic proof that the entire infinite towers of commuting gauge and string charges match); references adde

Black hole entropy reveals a 12th "dimension"

The Beckenstein-Hawking black hole entropy in string theory and its extensions, as expressed in terms of charges that correspond to central extensions of the supersymmetry algebra, has more symmetries than U-duality. It is invariant under transformations of the charges, involving a 12th (or 13th) ``dimension''. This is an indication that the secret theory behind string theory has a superalgebra involving Lorentz non-scalar extensions (that are not strictly central), as suggested in S-theory, and which could be hidden in M- or F- theories. It is suggested that the idea of spacetime is broader than usual, and that a larger ``spacetime" is partially present in black holes.Comment: Latex, 20 pages, minor formatting correction

Integrable Supersymmetric Fluid Mechanics from Superstrings

Following the construction of a model for the planar supersymmetric Chaplygin gas, supersymmetric fluid mechanics in (1+1)-dimensions is obtained from the light-cone parametrized Nambu-Goto superstring in (2+1)-dimensions. The lineal model is completely integrable and can be formulated neatly using Riemann coordinates. Infinite towers of conserved charges and supercharges are exhibited. They form irreducible representations of a dynamical (hidden) SO(2,1) symmetry group.Comment: 11 pages, LaTex; typographical errors correcte

Agri-environment Policy Design With Hidden Information and Hidden Action: Input Quotas vs Input Charges

Moxey, White and Ozanne (1999) have shown how transfer payments coupled with input quotas can be used to design optimal truth-telling mechanisms for voluntary agri-environmental schemes under hidden information about compliance costs. Ozanne, Hogan and Colman (2001) adapted the Moxey et al. model to analyze hidden action in such schemes, analyzing the relationships between input abatement, the cost of monitoring compliance and farmers’ risk preferences. White (2002) extended the Moxey et al. model to analyze the design of contracts under both hidden action and hidden information, but used an input charge/transfer payment approach rather than the original input quota/transfer payment one. In addition, he assumed that farmers caught cheating face a variable fine, related to the amount of input they apply in excess of the amount agreed in the contract, rather than a fixed fine as assumed by Ozanne et al. White argues that his results show that an input charge/transfer payment policy is more efficient than a quota when the regulator cannot observe compliance costs of individual farmers. This paper integrates the previous work, developing a model of both hidden action and hidden information in agri-environmental schemes based on the input quota/transfer payment approach of Moxey et al. (1999) and Ozanne et al. (2001), rather than the input charge/transfer payment approach of White (2002), but the variable fine of the latter rather than the fixed fine assumed by Ozanne et al. This integrated model shows that, contrary to White (2002), the input quota and input charges approaches lead to identical outcomes in terms of abatement levels, compensation payments, monitoring costs, probabilities and social welfare.Environmental Economics and Policy,