Momentum substitutions Sample Clauses

Momentum substitutions. After the Feynman rules have been applied, the integrals are in a form in which they can be converted to Forcer’s basis for the topologies. The reduction to this basis needs to be done with great care as it is quite easy to generate an extremely large number of terms. This process is split up into two components: rewriting the momenta to a momentum basis and rewriting the dot products to Forcer’s basis. The momentum basis should contain all the momenta of the irreducible dot products belonging to this Forcer topology. The other basis elements are obtained by an exhaustive search that tries to minimise the number of terms that will be created when rewriting to the basis. The optimisation criterion is the sum of the square of the number of terms that get created for all the momentum and dot product rewrites. In order to prevent a blow-up in the number of terms, we create a layered rewrite of momenta. This layering is constructed automatically and makes the momentum rewrites order dependent: p9.p?!{p9,}=+p2.p+p7.p+p11.p-Q.p; p5.p?!{p5,}=-p11.p-p3.p+Q.p; p6.p?!{p6,}=-p2.p+p3.p-p7.p; p1.p?!{p1,p4}=+Q.p-p8.p; p10.p?!{p10,}=+p2.p-p3.p; p4.p?!{p4,p1}=+p11.p+p3.p; p7.p?!{p7,}=+p8.p-p11.p; p9.p?!{p9,}=-p6.p-p5.p; p5.p?!{p5,}=-p4.p+Q.p; p6.p?!{p6,}=-p10.p-p7.p; p1.p?!{p1,p4}=+Q.p-p8.p; p10.p?!{p10,}=+p2.p-p3.p; p4.p?!{p4,p1}=+p11.p+p3.p; p7.p?!{p7,}=+p8.p-p11.p; Because some terms will merge during the momentum rewrites, the layered approach is much faster. Note that dot products will not be rewritten if they are elements of the dot product basis. Finally, the dot products are rewritten, straight to the internal Forcer notation. This is displayed in listing 3.10. Listing 3.10: Form code for dot product rewriting id Q.p1 = Q^2/2+i1/2-i8/2; id p1.p2 = i1/2+i2/2-i9/2; id p2.p3 = -i10/2+i2/2+i3/2; id Q.p4 = Q^2/2+i4/2-i5/2; id p3.p4 = -i11/2+i3/2+i4/2; id p1.p3 = -Q^2/2+i11/2+i13+i14-i4/2+i5/2-i7/2+i8/2; id p2.p4 = -Q^2/2-i1/2+i12+i13+i5/2-i6/2+i8/2+i9/2; We note that in the actual code there will be .sort statements between the id statements and that there are extra optimisations in place to prevent excessive term generation.‌
AutoNDA by SimpleDocs

Related to Momentum substitutions

  • VACANCIES, PROMOTIONS AND TRANSFERS A. The Board recognizes that it is desirable in making assignments to consider the interests and aspirations of its teachers. Requests by a teacher for a transfer to a different class, building, or position shall be made in writing, one copy of which shall be filed with the Superintendent. Such requests shall be renewed once each year to assure active consideration by the Board. The Board will give serious consideration to such requests.

  • User Contributions The Website may contain message boards, chat rooms, personal web pages or profiles, forums, bulletin boards, and other interactive features (collectively, "Interactive Services") that allow users to post, submit, publish, display, or transmit to other users or other persons (hereinafter, "post") content or materials (collectively, "User Contributions") on or through the Website. All User Contributions must comply with these Terms of Use. Any User Contribution you post to the site will be considered non-confidential and non- proprietary. By providing any User Contribution on the Website, you grant us and our affiliates and service providers, and each of their and our respective licensees, successors, and assigns the right to use, reproduce, modify, perform, display, distribute, and otherwise disclose to third parties any such material. You represent and warrant that: • You own or control all rights in and to the User Contributions and have the right to grant the license granted above to us and our affiliates and service providers, and each of their and our respective licensees, successors, and assigns. • All of your User Contributions do and will comply with these Terms of Use. You understand and acknowledge that you are responsible for any User Contributions you submit or contribute, and you, not the Company, have full responsibility for such content, including its legality, reliability, accuracy, and appropriateness. We are not responsible or liable to any third party for the content or accuracy of any User Contributions posted by you or any other user of the Website.

  • UNE Port/Loop Combinations 5.3.1 Combinations of port and loop unbundled Network Elements along with switching and transport unbundled Network Elements provide local exchange service for the origination or termination of calls. Port/loop combinations support the same local calling and feature requirements as described in the Unbundled Local Switching or Port section of this Attachment and the ability to presubscribe to a primary carrier for intraLATA toll service and/or to presubscribe to a primary carrier for interLATA toll service.

  • When Can I Make Contributions You may make annual contributions to your Xxxx XXX any time up to and including the due date for filing your tax return for the year, not including extensions. You may continue to make regular contributions to your Xxxx XXX even after you attain RMD age. In addition, rollover contributions and transfers (to the extent permitted as discussed below) may be made at any time, regardless of your age.

  • IN-KIND DISTRIBUTIONS Subject to Section 00-00-000 of the Act, the Company may make in-kind distributions of the Company assets, provided the Members unanimously agree and such agreement is in writing. The fair market value of the property must be determined and agreed upon by the Members before the distribution is made. The receiving Member’s capital account shall be adjusted to reflect the value of the in-kind distribution.

  • Grading systems of the institutions [It is recommended that receiving institutions provide the statistical distribution of grades according to the descriptions in the ECTS users’ guide7. A link to a webpage can be enough. The table will facilitate the interpretation of each grade awarded to students and will facilitate the credit transfer by the sending institution.]

  • VACANCIES AND TRANSFERS A vacancy shall be defined, for purposes of this Agreement, as a position previously held by a bargaining unit member that needs to be filled, or a newly created PSS position. When all necessary parties agree, vacancies can be filled by organizational advancement or transfer from within the hiring department and shall not require posting. All vacancies will be posted for a minimum of seven (7) working days unless filled by transfer, reassignment, or recall of a laid off staff member. Notice of vacancies will be given to the Alliance President and Chief Alliance Xxxxxxx at the time they are posted on the University's electronic Notices GVSU Business board, and will be simultaneously posted at the University’s electronic employment website. A vacancy will not be filled until after the posting period has expired. Job postings shall include the classification, department, location(s), work schedule and the position description. The search committee will include a PSS member. Typically, vacancies will be posted as an open search available for both internal and external applicants. A job posting limited to internal applicants may occur upon approval. In each instance, all qualified internal applicants will receive an interview. The search committee must present strong justification for not selecting an internal applicant who meets the minimum qualifications of the position. When two applicants are equally qualified for the vacant position, based on current position description and satisfactory work and attendance, the more senior qualified staff member will receive the assignment. At the time of job offer, the University shall notify the selected staff member of any known or impending changes in the position. The Human Resources Office, or their designee, will provide internal applicants not selected for the position with rationale for the decision. Candidates who were interviewed but not selected may contact Human Resources to schedule a meeting with the Search Committee Chairperson, a Human Resource representative, and an Alliance Representative to discuss the reason for non-selection. The Alliance must notify the employer within three (3) working days that the meeting has been the step 1 meeting of the grievance process. If a meeting is requested or a grievance is filed, the position cannot be filled until this process is completed. An internal staff member selected for the position will be required to establish that they can do the job within eight (8) working days. Failure to qualify shall result in returning the selected staff member to their former position and is not subject to the grievance procedure. The staff member shall also have the option to elect to return to their former position within eight (8) working days. When making departmental changes, transfer shall be with the consent of the staff member whenever possible but when there is no reasonable alternative, it may be involuntary. When involuntary transfer is required, the least senior qualified staff member shall be transferred to a similar position (e.g., classification, full or part-time) or be given the option of electing an unpaid leave of absence with eligibility only for the next vacancy in their classification, if qualified. That person shall be disqualified from consideration when the position from which they were transferred is posted. Nothing contained in this Section is intended to prevent the University from making necessary changes in positions, eliminating positions or creating new positions.

  • Allocations of Profits and Losses Except as otherwise provided in this Agreement, Profits and Losses (and, to the extent necessary, individual items of income, gain or loss or deduction of the Partnership) shall be allocated in a manner such that the Capital Account of each Partner after giving effect to the Special Allocations set forth in Section 5.05 is, as nearly as possible, equal (proportionately) to (i) the distributions that would be made pursuant to Article IV if the Partnership were dissolved, its affairs wound up and its assets sold for cash equal to their Carrying Value, all Partnership liabilities were satisfied (limited with respect to each non-recourse liability to the Carrying Value of the assets securing such liability) and the net assets of the Partnership were distributed to the Partners pursuant to this Agreement, minus (ii) such Partner’s share of Partnership Minimum Gain and Partner Nonrecourse Debt Minimum Gain, computed immediately prior to the hypothetical sale of assets. For purposes of this Article V, each Unvested Unit shall be treated as a Vested Unit. Notwithstanding the foregoing, the General Partner shall make such adjustments to Capital Accounts as it determines in its sole discretion to be appropriate to ensure allocations are made in accordance with a partner’s interest in the Partnership.

  • Commingling, Exchange and Investment of the Contributions 2.1. The Contributions shall be accounted for as a single trust fund and shall be kept separate and apart from the funds of the Bank. The Contributions may be commingled with other trust fund assets maintained by the Bank.

  • Terminal Transfers You can get a receipt at the time you make any transfer at a First Hawaiian ATM, Network ATM, or POS terminal.

Time is Money Join Law Insider Premium to draft better contracts faster.